We discuss two alternate spectrum-based estimators of the bivariate Hurst exponent in the power-law cross-correlations setting, the cross-periodogram and local $X$-Whittle estimators, as generalizations of their univariate counterparts. As the spectrum-based estimators are dependent on a part of the spectrum taken into consideration during estimation, a simulation study showing performance of the estimators under varying bandwidth parameter as well as correlation between processes and their specification is provided as well. These estimators are less biased than the already existent averaged periodogram estimator, which, however, has slightly lower variance. The spectrum-based estimators can serve as a good complement to the popular time domain estimators.

We construct higher-order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps: (i) the time-independent expulsive trap, (ii) time-dependent monotonous trap, and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second- and third-order rogue waves transform into the first-order-like rogue waves. We also analyze the density profiles of breather solutions. Here we also show that the shapes of the breathers change when we tune the strength of the trap parameter. Our results may help to manage rogue waves experimentally in a BEC system.

The detection of a nonrandom structure from experimental data can be crucial for the classification, understanding, and interpretation of the generating process. We here introduce a rank-based nonlinear predictability score to detect determinism from point process data. Thanks to its modular nature, this approach can be adapted to whatever signature in the data one considers indicative of deterministic structure. After validating our approach using point process signals from deterministic and stochastic model dynamics, we show an application to neuronal spike trains recorded in the brain of an epilepsy patient. While we illustrate our approach in the context of temporal point processes, it can be readily applied to spatial point processes as well.

A compact Z-pinch x-ray hohlraum design with parallel-driven x-ray sources is experimentally demonstrated in a configuration with a central target and tailored shine shields at a 1.7-MA Zebra generator. Driving in parallel two magnetically decoupled compact double-planar-wire Z pinches has demonstrated the generation of synchronized x-ray bursts that correlated well in time with x-ray emission from a central reemission target. Good agreement between simulated and measured hohlraum radiation temperature of the central target is shown. The advantages of compact hohlraum design applications for multi-MA facilities are discussed.

A phenomenon resembling natural ball lightning can be produced via electrical arcing through silicon. We use lump silicon instead of silicon wafers to achieve higher production rates and larger, longer-lived luminous balls than previously reported. The luminous balls consist of a silicon core surrounded by a porous network of loosely bound silicon dioxide nanoparticles. We find that the balls carry a small net charge on the order of ${10}^{-12}$ C and propose that the nanoparticles are electrostatically bound to the core due to this charge.

Molecular dynamics (MD) simulations are coupled to solutions of Poisson's equation to study the effects of the electrical boundary conditions on the emission modes of an electrospray thruster fed with an ionic liquid. A comparison of a new tip boundary condition with an analytical model based on a semihyperboloidal shape offers good agreement, although the analytical model overestimates the maximum value of the tangential electric field since it does not take into account the space charge that reduces the field at the liquid surface. It is found that a constant electric field model gives similar agreement to the more rigorous and computationally expensive tip boundary condition at lower flow rates. However, at higher mass flow rates the constant electric field produces extruded particles with higher Coulomb energy per ion, consistent with droplet formation. Furthermore, the MD simulations show that ion emission sites differ based on the boundary condition and snapshots offer an explanation as to why some boundary condition models will predict emission in a purely ionic mode, whereas others suggest a mixed ion-droplet regime. Finally, specific impulses and thrusts are compared for the different models and are found to vary up to 30% due to differences in the average charge to mass ratio.

In phase-transition phenomena, the estimation of the critical point is crucial for the calculation of the various critical exponents and the determination of the universality class they belong to. However, this is not an easy task, since a large amount of realizations is needed to eliminate the noise in the data. In this paper, we introduce a novel method for the simultaneous estimation of the critical point $p_c$ and the critical exponent $\beta /\nu$, applied for the case of “explosive” bond percolation on two-dimensional square lattices and Erdös-Rényi networks. The results show that with only a few hundred realizations, it is possible to acquire accurate values for these quantities. Guidelines are given at the end for the applicability of the method to other cases as well.

We study the evolution of cooperation in spatial prisoner's dilemma games with and without extortion by adopting the aspiration-driven strategy updating rule. We focus explicitly on how the strategy updating manner (whether synchronous or asynchronous) and also the introduction of extortion strategy affect the collective outcome of the games. By means of Monte Carlo simulations as well as dynamical cluster techniques, we find that the involvement of extortioners facilitates the boom of cooperators in the population (and whom can always dominate the population if the temptation to defect is not too large) for both synchronous and asynchronous strategy updating, in stark contrast to the other case, where cooperation is promoted for an intermediate aspiration level with synchronous strategy updating, but is remarkably inhibited if the strategy updating is implemented asynchronously. We explain the results by configurational analysis and find that the presence of extortion leads to the checkerboard-like ordering of cooperators and extortioners, which enable cooperators to prevail in the population with both strategy updating manners. Moreover, extortion itself is evolutionary stable, and therefore acts as the incubator for the evolution of cooperation.

We investigate the dynamical phase diagram of the generalized Langevin equation of the free particle driven by a Mittag-Leffler noise and show critical curves and a critical value of the exponent parameter of the Mittag-Leffler function that mark different dynamical regimes. By considering that the modeling of a Mittag-Leffer memory kernel corresponds to a power-law second-order memory kernel, we show that the generalized Langevin equation of the velocity autocorrelation function (VACF) is transformed in a fractional Langevin equation. In the superdiffusive case our results exhibit oscillations and negative correlations of the VACF that are not provided by the usual power-law noise model.

We consider an exclusion process on a ring in which a particle hops to an empty neighboring site with a rate that depends on the number of vacancies $n$ in front of it. In the steady state, using the well-known mapping of this model to the zero-range process, we write down an exact formula for the partition function and the particle-particle correlation function in the canonical ensemble. In the thermodynamic limit, we find a simple analytical expression for the generating function of the correlation function. This result is applied to the hop rate $u\left(n\right)=1+(b/n)$ for which a phase transition between high-density laminar phase and low-density jammed phase occurs for $b>2$. For these rates, we find that at the critical density, the correlation function decays algebraically with a continuously varying exponent $b-2$. We also calculate the two-point correlation function above the critical density and find that the correlation length diverges with a critical exponent $\nu =1/(b-2)$ for $b<3$ and 1 for $b>3$. These results are compared with those obtained using an exact series expansion for finite systems.

We reexamine the two-dimensional linear $\mathrm{O}\left(2\right)$ model (${\phi }^4$ theory) in the framework of the nonperturbative renormalization-group. From the flow equations obtained in the derivative expansion to second order and with optimization of the infrared regulator, we find a transition between a high-temperature (disordered) phase and a low-temperature phase displaying a line of fixed points and algebraic order. We obtain a picture in agreement with the standard theory of the Kosterlitz-Thouless (KT) transition and reproduce the universal features of the transition. In particular, we find the anomalous dimension $\eta \left(T_{\mathrm{KT}}\right)\simeq 0.24$ and the stiffness jump ${\rho }_s\left(T_{\mathrm{KT}}^{-}\right)\simeq 0.64$ at the transition temperature $T_{\mathrm{KT}}$, in very good agreement with the exact results $\eta \left(T_{\mathrm{KT}}\right)=1/4$ and ${\rho }_s\left(T_{\mathrm{KT}}^{-}\right)=2/\pi$, as well as an essential singularity of the correlation length in the high-temperature phase as $T\to T_{\mathrm{KT}}$.

As a generic example for crystals where the crystal-fluid interface tension depends on the orientation of the interface relative to the crystal lattice axes, the nearest-neighbor Ising model on the simple cubic lattice is studied over a wide temperature range, both above and below the roughening transition temperature. Using a thin-film geometry $L_x\times L_y\times L_z$ with periodic boundary conditions along the $z$ axis and two free $L_x\times L_y$ surfaces at which opposing surface fields $\pm H_1$ act, under conditions of partial wetting, a single planar interface inclined under a contact angle $\theta <\pi /2$ relative to the $yz$ plane is stabilized. In the $y$ direction, a generalization of the antiperiodic boundary condition is used that maintains the translational invariance in the $y$ direction despite the inhomogeneity of the magnetization distribution in this system. This geometry allows a simultaneous study of the angle-dependent interface tension, the contact angle, and the line tension (which depends on the contact angle, and on temperature). All these quantities are extracted from suitable thermodynamic integration procedures. In order to keep finite-size effects as well as statistical errors small enough, rather large lattice sizes (of the order of 46 million sites) were found to be necessary, and the availability of very efficient code implementation of graphics processing units was crucial for the feasibility of this study.

We propose a physically realizable Maxwell's demon device using a spin valve interacting unitarily for a short time with electrons placed on a tape of quantum dots, which is thermodynamically equivalent to the device introduced by Mandal and Jarzynski [D. Mandal and C. Jarzynski, Proc. Natl. Acad. Sci. USA 109, 11641 (2012)]. The model is exactly solvable and we show that it can be equivalently interpreted as a Brownian ratchet demon. We then consider a measurement-based discrete feedback scheme, which produces identical system dynamics, but possesses a different second law inequality. We show that the second law for discrete feedback control can provide a smaller, equal, or larger bound on the maximum extractable work as compared to the second law involving the tape of bits. Finally, we derive an effective master equation governing the system evolution for Poisson distributed bits on the tape (or measurement times, respectively) and we show that its associated entropy production rate contains the same physical statement as the second law involving the tape of bits.

We present an x-ray microtomography study of the three-dimensional structural correlations in monodisperse granular packings. By measuring an orientation-dependent pair correlation function, we find that the local structure shows an angularly anisotropic orientation correlation. The correlation is strongest along the major axis of the local Minkowski tensor of the Voronoi cell. It turns out that this anisotropic correlation is consistent with the existence of some locally favored structures. The study suggests the importance of high-order structural correlations in random granular packings.

We study the penetration dynamics of a projectile incident normally on a substrate comprising of smaller granular particles in three-dimensions using the discrete element method. Scaling of the penetration depth is consistent with experimental observations for small velocity impacts. Our studies are consistent with the observation that the normal or drag force experienced by the penetrating grain obeys the generalized Poncelet law, which has been extensively invoked in understanding the drag force in the recent experimental data. We find that the normal force experienced by the projectile consists of position and kinetic-energy-dependent pieces. Three different penetration regimes are identified in our studies for low-impact velocities. The first two regimes are observed immediately after the impact and in the early penetration stage, respectively, during which the drag force is seen to depend on the kinetic energy. The depth dependence of the drag force becomes significant in the third regime when the projectile is moving slowly and is partially immersed in the substrate. These regimes relate to the different configurations of the bed: the initial loose surface packed state, fluidized bed below the region of impact, and the state after the crater formation commences.

In this paper we investigate the statistical behavior of an annealed continuous damage model. For different model variations we study distributions of times to failure and compare these results with the classical case of metastable nucleation in statistical physics. We show that our model has a tuning parameter, related to the degree of damage reversibility, that determines the model's behavior. Depending on the value of this parameter, our model exhibits statistical behavior either similar to classical reversible nucleation phenomena in statistical physics or to an absolutely different type of behavior intrinsic to systems with damage. This comparison allows us to investigate possible similarities and differences between damage phenomena and reversible nucleation.

We study the topology of the $\mathbf{c}$-director field near topological defects with point core and with a droplet in the core of the defect in nonpolar smectic-$C$ and ferroelectric smectic-$C*$ freestanding films using polarized optical microscopy. Free and confined geometry of topological defects and droplets with strong outer boundary condition are compared. The $\mathbf{c}$-director field can be remarkably different around a point defect and a droplet with the same topological charge $S=+1$. In ferroelectric films, splay deformation of the $\mathbf{c}$-director transforms into bend deformation after droplet nucleation. Heating a ferroelectric film with an $S=+1$ droplet leads to a dramatic change of the $\mathbf{c}$-director topology from bend to splay. In confined geometry we found spiral structures in which the $\mathbf{c}$-director has opposite direction of rotation along the inner and outer boundaries of the island. Our observations are discussed on the basis of theories taking into account both the influence of polarity and of confined geometry on elasticity and topology of the $\mathbf{c}$-director field.

The thermodynamic and conformational properties of catenated double-ring A-B copolymer melts are investigated through lattice Monte Carlo simulations. The topological constraint on the catenated copolymers is shown to suppress demixing of A and B monomers. This action results in their order-to-disorder transition (ODT) at an increased segregation level and the lamellae below ODT with reduced order, when compared to diblock copolymers of linear or single-ring topology. The A and B rings are pulled closer by catenation in the copolymer, which leads to its smaller gyration radius, lamellar domain spacing, and distance between mass centers of the two rings than for the diblock copolymers. With increasing segregation tendencies, the gyration radii of the A rings of the catenated copolymers stretch along the direction normal to lamellae, while the A-block conformations of the single-ring copolymers change their shapes from ellipsoid to sphere.

The mayfly nymph breathes under water through an oscillating array of plate-shaped tracheal gills. As the nymph grows, the kinematics of these gills change abruptly from rowing to flapping. The classical fluid dynamics approach to consider the mayfly nymph as a pumping device fails in giving clear reasons for this switch. In order to shed some light on this switch between the two distinct kinematics, we analyze the problem under a Lagrangian viewpoint. We consider that a good Lagrangian transport that effectively distributes and stirs water and dissolved oxygen between and around the gills is the main goal of the gill motion. Using this Lagrangian approach, we are able to provide possible reasons behind the observed switch from rowing to flapping. More precisely, we conduct a series of in silico mayfly nymph experiments, where body shape, as well as gill shapes, structures, and kinematics are matched to those from in vivo. In this paper, we show both qualitatively and quantitatively how the change of kinematics enables better attraction, confinement, and stirring of water charged of dissolved oxygen inside the gills area. We reveal the attracting barriers to transport, i.e., attracting Lagrangian coherent structures, that form the transport skeleton between and around the gills. In addition, we quantify how well the fluid particles are stirred inside the gills area, which by extension leads us to conclude that it will increase the proneness of molecules of dissolved oxygen to be close enough to the gills for extraction.

We consider clustering of particles in the lattice gas model above the critical point. We find the probability for large density fluctuations over scales much larger than the correlation length. This fundamental problem is of interest in various biological contexts such as quorum sensing and clustering of motile, adhesive, cancer cells. In the latter case, it may give a clue to the problem of growth of recurrent tumors. We develop a formalism for the analysis of this rare event employing a phenomenological master equation and measuring the transition rates in numerical simulations. The spontaneous clustering is treated in the framework of the eikonal approximation to the master equation.