We present the results of an experimental study of the elastic enhancement factor $W$ for a microwave rectangular cavity simulating a two-dimensional quantum billiard in a transient region between regular and chaotic dynamics. The cavity was coupled to a vector network analyzer via two microwave antennas. The departure of the system from an integrable one due to the presence of antennas acting as scatterers is characterized by the parameter of chaoticity $\kappa =2.8$. The experimental results for the rectangular cavity are compared with those obtained for a microwave rough cavity simulating a chaotic quantum billiard. The experimental results were obtained for the frequency range $\nu =16\text{–}18.5$ GHz and moderate absorption strength $\gamma =5.2\text{–}7.4$. We show that the elastic enhancement factor for the rectangular cavity lies below the theoretical value $W=3$ predicted for integrable systems, and it is significantly higher than that obtained for the rough cavity. The results obtained for the microwave rough cavity are smaller than those obtained within the framework of random matrix theory, and they lie between them and those predicted within a recently introduced model of the two-channel coupling [V. V. Sokolov and O. V. Zhirov, arXiv:1411.6211 [nucl-th]].

Spatiotemporal chaos in oscillatory and excitable media is often characterized by the presence of phase singularities called defects. Understanding such defect-mediated turbulence and its dependence on the dimensionality of a given system is an important challenge in nonlinear dynamics. This is especially true in the context of ventricular fibrillation in the heart, where the importance of the thickness of the ventricular wall is contentious. Here, we study defect-mediated turbulence arising in two different regimes in a conceptual model of excitable media and investigate how the statistical character of the turbulence changes if the thickness of the medium is changed from (quasi-) two- dimensional to three dimensional. We find that the thickness of the medium does not have a significant influence in, far from onset, fully developed turbulence while there is a clear transition if the system is close to a spiral instability. We provide clear evidence that the observed transition and change in the mechanism that drives the turbulent behavior is purely a consequence of the dimensionality of the medium. Using filament tracking, we further show that the statistical properties in the three-dimensional medium are different from those in turbulent regimes arising from filament instabilities like the negative line tension instability. Simulations also show that the presence of this unique three-dimensional turbulent dynamics is not model specific.

The atmosphere is a nonlinear stratified fluid in which internal gravity waves are present. These waves interact with the flow, resulting in wave turbulence that displays important differences with the turbulence observed in isotropic and homogeneous flows. We study numerically the role of these waves and their interaction with the large-scale flow, consisting of vertically sheared horizontal winds. We calculate their space- and time-resolved energy spectrum (a four-dimensional spectrum) and show that most of the energy is concentrated along a dispersion relation that is Doppler shifted by the horizontal winds. We also observe that when uniform winds are let to develop in each horizontal layer of the flow, waves whose phase velocity is equal to the horizontal wind speed have negligible energy. This indicates a nonlocal transfer of their energy to the mean flow. Both phenomena, the Doppler shift and the absorption of waves traveling with the wind speed, are not accounted for in current theories of stratified wave turbulence.

The hydrodynamic reciprocal theorem for Stokes flows is generalized to incorporate the Navier slip boundary condition, which can be derived from Onsager's variational principle of least energy dissipation. The hydrodynamic reciprocal relations and the Jeffery orbit, both of which arise from the motion of a slippery anisotropic particle in a simple viscous shear flow, are investigated theoretically and numerically using the fluid particle dynamics method [Phys. Rev. Lett. 85, 1338 (2000)]. For a slippery elliptical particle in a linear shear flow, the hydrodynamic reciprocal relations between the rotational torque and the shear stress are studied and related to the Jeffery orbit, showing that the boundary slip can effectively enhance the anisotropy of the particle. Physically, by replacing the no-slip boundary condition with the Navier slip condition at the particle surface, the cross coupling between the rotational torque and the shear stress is enhanced, as manifested through a dimensionless parameter in both of the hydrodynamic reciprocal relations and the Jeffery orbit. In addition, simulations for a circular particle patterned with portions of no-slip and Navier slip are carried out, showing that the particle possesses an effective anisotropy and follows the Jeffery orbit as well. This effective anisotropy can be tuned by changing the ratio of no-slip portion to slip potion. The connection of the present work to nematic liquid crystals' constitutive relations is discussed.

To describe the small-scale intermittency of turbulence, a self-similarity is assumed for the probability density function of a logarithm of the rate of energy dissipation smoothed over a length scale among those in the inertial range. The result is an extension of Kolmogorov's classical theory [A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 301 (1941)], i.e., a one-parameter framework where the logarithm obeys some stable distribution. Scaling laws are obtained for the dissipation rate and for the two-point velocity difference. They are consistent with theoretical constraints and with the observed scaling laws. Also discussed is the physics that determines the value of the parameter.

Particles in turbulence live complicated lives. It is nonetheless sometimes possible to find order in this complexity. It was proposed in Falkovich et al. [Phys. Rev. Lett. 110, 214502 (2013)] that pairs of Lagrangian tracers at small scales, in an incompressible isotropic turbulent flow, have a statistical conservation law. More specifically, in a $d$-dimensional flow the distance $R\left(t\right)$ between two neutrally buoyant particles, raised to the power $-d$ and averaged over velocity realizations, remains at all times equal to the initial, fixed, separation raised to the same power. In this work we present evidence from direct numerical simulations of two- and three-dimensional turbulence for this conservation. In both cases the conservation is lost when particles exit the linear flow regime. In two dimensions we show that, as an extension of the conservation law, an Evans-Cohen-Morriss or Gallavotti-Cohen type fluctuation relation exists. We also analyze data from a 3D laboratory experiment [Liberzon et al., Physica D 241, 208 (2012)], finding that although it probes small scales they are not in the smooth regime. Thus instead of $\langle R^{-3}\rangle$, we look for a similar, power-law-in-separation conservation law. We show that the existence of an initially slowly varying function of this form can be predicted but that it does not turn into a conservation law. We suggest that the conservation of $\langle R^{-d}\rangle$, demonstrated here, can be used as a check of isotropy, incompressibility, and flow dimensionality in numerical and laboratory experiments that focus on small scales.

We determine the viscosity parameters of the multiparticle collision dynamics (MPC) approach, a particle-based mesoscale hydrodynamic simulation method for fluids. We perform analytical calculations and verify our results by simulations. The stochastic rotation dynamics and the Andersen thermostat variant of MPC are considered, both with and without angular momentum conservation. As an important result, we find a nonzero bulk viscosity for every MPC version. The explicit calculation shows that the bulk viscosity is determined solely by the collisional interactions of MPC.

We present a simple, fast, and promising method to compute the melting curves of materials with ab initio molecular dynamics. It is based on the two-phase thermodynamic model of Lin et al [J. Chem. Phys. 119, 11792 (2003)] and its improved version given by Desjarlais [Phys. Rev. E 88, 062145 (2013)]. In this model, the velocity autocorrelation function is utilized to calculate the contribution of the nuclei motion to the entropy of the solid and liquid phases. It is then possible to find the thermodynamic conditions of equal Gibbs free energy between these phases, defining the melting curve. The first benchmark on the face-centered cubic melting curve of aluminum from 0 to 300 GPa demonstrates how to obtain an accuracy of 5%–10%, comparable to the most sophisticated methods, for a much lower computational cost.

Trachenko et al. [Phys. Rev. E 89, 032126 (2014)] have argued for the existence of a “Frenkel line” in fluid hydrogen that separates “rigid” and “nonrigid” regimes in a supercritical region. On that basis, they proposed a criterion for locating the boundary between the interior and the atmosphere for gas giants. This Comment shows that the two methods they use to locate the transition between the rigid and nonrigid states are both questionable, which casts doubt on the claims in the paper.

We have recently proposed the dynamic transition of molecular hydrogen in gas giants around 10 GPa based on the recent understanding of a supercritical state related to the Frenkel line. In the preceding Comment, Bryk makes several remarks with regard to the Frenkel line and its relationship to the speed of sound. We disagree with this discussion and respond to it in this Reply.

In this paper, we extend the studies on the emergent thermodynamics in a quenched quantum Ising chain (QIC) [R. Dorner, J. Goold, C. Cormick, M. Paternostro, and V. Vedral, Phys. Rev. Lett. 109, 160601 (2012)] to a more general quantum spin chain with asymmetrical excitation spectra. We verify that the Jarzynski and Tasaki-Crooks relations are still tenable in this system. As an example, we discuss the behaviors of the work done and irreversible entropy production induced by a sudden quenching in the anisotropic XY chain in a transverse field with the XZY-YZX type of three-site interactions. Different from the QIC, this system has the phase transitions not only between two gapped phases, but also between gapped (or gapless) and gapless phases at zero temperature. We discuss the effects of quantum phase transitions on the work done and irreversible entropy production at low temperature.

Fixed-point distributions for the couplings of Ising spin glasses with nearest-neighbor interactions on hierarchical lattices are investigated numerically. Hierarchical lattices within the Migdal-Kadanoff family with fractal dimensions in the range $2.58\le D\le 7$, as well as a lattice of the Wheatstone-Bridge family with fractal dimension $D\approx 3.58$ are considered. Three initial distributions for the couplings are analyzed, namely, the Gaussian, bimodal, and uniform ones. In all cases, after a few iterations of the renormalization-group procedure, the associated probability distributions approached universal fixed shapes. For hierarchical lattices of the Migdal-Kadanoff family, the fixed-point distributions were well fitted either by stretched exponentials, or by $q$-Gaussian distributions; both fittings recover the expected Gaussian limit as $D\to \infty$. In the case of the Wheatstone-Bridge lattice, the best fit was found by means of a stretched-exponential distribution.

The individual motion of a colloidal particle is described by an overdamped Langevin equation. When rotational degrees of freedom are relevant, these are described by a corresponding Langevin process. Our purpose is to show that the microscopic local density of colloids, in terms of a space and rotation state, also evolves according to a Langevin equation. The latter can then be used as the starting point of a variety of approaches, ranging from dynamical density functional theory to mode-coupling approximations.

We describe the effect of power-law initial distributions of clusters on ordinary percolation and its generalizations, specifically, models of explosive percolation processes based on local optimization. These aggregation processes were shown to exhibit continuous phase transitions if the evolution starts from a set of disconnected nodes. Since the critical exponents of the order parameter in explosive percolation transitions turned out to be very small, these transitions were first believed to be discontinuous. In this article we analyze the evolution starting from clusters of nodes whose sizes are distributed according to a power law. We show that these initial distributions change dramatically the position and order of the phase transitions in these problems. We find a particular initial power-law distribution producing a peculiar effect on explosive percolation, namely, before the emergence of the percolation cluster, the system is in a “critical phase” with an infinite generalized susceptibility. This critical phase is absent in ordinary percolation models with any power-law initial conditions. The transition from the critical phase is an infinite-order phase transition, which resembles the scenario of the Berezinskii-Kosterlitz-Thouless phase transition. We obtain the critical singularity of susceptibility at this peculiar infinite-order transition in explosive percolation. It turns out that susceptibility in this situation does not obey the Curie-Weiss law.

We examine the mobility and velocity fluctuations of a driven particle moving through an active matter bath of self-mobile disks for varied density or area coverage and varied activity. We show that the driven particle mobility can exhibit nonmonotonic behavior that is correlated with distinct changes in the spatiotemporal structures that arise in the active media. We demonstrate that the probe particle velocity distributions exhibit specific features in the different dynamic regimes and identify an activity-induced uniform crystallization that occurs for moderate activity levels and is distinct from the previously observed higher activity cluster phase. The velocity distribution in the cluster phase has telegraph noise characteristics produced when the probe particle moves alternately through high-mobility areas that are in the gas state and low-mobility areas that are in the dense phase. For higher densities and large activities, the system enters what we characterize as an active jamming regime. Here the probe particle moves in intermittent jumps or avalanches that have power-law-distributed sizes that are similar to the avalanche distributions observed for nonactive disk systems near the jamming transition.

The role played by side-chain interactions on the formation of $\alpha$-helices is studied using extensive all-atom molecular dynamics simulations of polyalanine-like peptides in explicit TIP4P water. The peptide is described by the OPLS-AA force field except for the Lennard-Jones interaction between $C_{\beta }-C_{\beta }$ atoms, which is modified systematically. We identify values of the Lennard-Jones parameter that promote $\alpha$-helix formation. To rationalize these results, potentials of mean force (PMF) between methane-like molecules that mimic side chains in our polyalanine-like peptides are computed. These PMF exhibit a complex distance dependence where global and local minima are separated by an energy barrier. We show that $\alpha$-helix propensity correlates with values of these PMF at distances corresponding to $C_{\beta }\text{–}{C}_{\beta }$ of $i-i+3$ and other nearest neighbors in the $\alpha$-helix. In particular, the set of Lennard-Jones parameters that promote $\alpha$-helices is characterized by PMF that exhibit a global minimum at distances corresponding to $i-i+3$ neighbors in $\alpha$-helices. Implications of these results are discussed.

Many physical, chemical, and biological systems exhibit traveling waves as a result of either an oscillatory instability or excitability. In the latter case a large multiplicity of stable spatially localized wavetrains consisting of different numbers of traveling pulses may be present. The existence of these states is related here to the presence of homoclinic snaking in the vicinity of a subcritical, finite wavenumber Hopf bifurcation. The pulses are organized in a slanted snaking structure resulting from the presence of a heteroclinic cycle between small and large amplitude traveling waves. Connections of this type require a multivalued dispersion relation. This dispersion relation is computed numerically and used to interpret the profile of the pulse group. The different spatially localized pulse trains can be accessed by appropriately customized initial stimuli, thereby blurring the traditional distinction between oscillatory and excitable systems. The results reveal a new class of phenomena relevant to spatiotemporal dynamics of excitable media, particularly in chemical and biological systems with multiple activators and inhibitors.

This paper presents numerical linear stability analysis of a cylindrical Taylor-Couette flow of liquid metal carrying axial electric current in a generally helical external magnetic field. Axially symmetric disturbances are considered in the inductionless approximation corresponding to zero magnetic Prandtl number. Axial symmetry allows us to reveal an entirely new electromagnetic instability. First, we show that the electric current passing through the liquid can extend the range of helical magnetorotational instability (HMRI) indefinitely by transforming it into a purely electromagnetic instability. Two different electromagnetic instability mechanisms are identified. The first is an internal pinch-type instability, which is due to the interaction of the electric current with its own magnetic field. Axisymmetric mode of this instability requires a free-space component of the azimuthal magnetic field. When the azimuthal component of the magnetic field is purely rotational and the axial component is nonzero, a new kind of electromagnetic instability emerges. The latter, driven by the interaction of electric current with a weak collinear magnetic field in a quiescent fluid, gives rise to a steady meridional circulation coupled with azimuthal rotation.

We introduce a ladder-shaped chain with each rung carrying a parity-time- $\left(\mathcal{PT}\text{−}\right)$ symmetric gain-loss dimer. The polarity of the dimers is staggered along the chain, meaning alternation of gain-loss and loss-gain rungs. This structure, which can be implemented as an optical waveguide array, is the simplest one which renders the system $\mathcal{PT}$-symmetric in both horizontal and vertical directions. The system is governed by a pair of linearly coupled discrete nonlinear Schrödinger equations with self-focusing or defocusing cubic onsite nonlinearity. Starting from the analytically tractable anticontinuum limit of uncoupled rungs and using the Newton's method for continuation of the solutions with the increase of the inter-rung coupling, we construct families of $\mathcal{PT}$-symmetric discrete solitons and identify their stability regions. Waveforms stemming from a single excited rung and double ones are identified. Dynamics of unstable solitons is investigated too.

A method for quantitative analysis of local pattern strength and defects in surface self-assembly imaging is presented and applied to images of stripe and hexagonal ordered domains. The presented method uses “shapelet” functions which were originally developed for quantitative analysis of images of galaxies $(\propto {10}^{20}\mathrm{m})$. In this work, they are used instead to quantify the presence of translational order in surface self-assembled films $(\propto {10}^{-9}\mathrm{m})$ through reformulation into “steerable” filters. The resulting method is computationally efficient (with respect to the number of filter evaluations), robust to variation in pattern feature shape, and, unlike previous approaches, is applicable to a wide variety of pattern types. An application of the method is presented which uses a nearest-neighbor analysis to distinguish between uniform (defect-free) and nonuniform (strained, defect-containing) regions within imaged self-assembled domains, both with striped and hexagonal patterns.