Spontaneous explosive emergent behavior takes place in heterogeneous networks when the frequencies of the nodes are positively correlated to the node degree. A central feature of such explosive transitions is a hysteretic behavior at the transition to synchronization. We unravel the underlying mechanisms and show that the dynamical origin of the hysteresis is a change of basin of attraction of the synchronization state. Our findings hold for heterogeneous networks with star graph motifs such as scale-free networks, and hence, reveal how microscopic network parameters such as node degree and frequency affect the global network properties and can be used for network design and control.

We consider homogeneous shear-stratified turbulence in a rotating frame, that exhibits complex nonlinear dynamics. Since the analysis of relative orientation between coupled fluctuating fields helps us to understand turbulence dynamics, we focus on the alignment properties of both the velocity and gravity fields with the potential vorticity gradient. With the help of statistical mechanics, we define a vector field which plays a role in the analogous so-called cross-helicity in magnetohydrodynamics. High-resolution direct numerical simulations of developed homogeneous baroclinic turbulence are performed, and a detailed analysis of probability density functions for cross-helicity is provided. A net preference for positive cross-helicity is shown to be related to a new alignment mechanism. We argue that the analysis of cross-helicity is crucial for understanding the dynamics of buoyancy driven flows.

The effects of noise on the dynamics of nonlinear systems is known to lead to many counterintuitive behaviors. Using simple planar limit cycle oscillators, we show that the addition of moderate noise leads to qualitatively different dynamics. In particular, the system can appear bistable, rotate in the opposite direction of the deterministic limit cycle, or cease oscillating altogether. Utilizing standard techniques from stochastic calculus and recently developed stochastic phase reduction methods, we elucidate the mechanisms underlying the different dynamics and verify our analysis with the use of numerical simulations. Last, we show that similar bistable behavior is found when moderate noise is applied to the FitzHugh-Nagumo model, which is more commonly used in biological applications.

We report new measurements of single particle dispersion in turbulent two-dimensional (2D) flows. Laboratory experiments in electromagnetically driven and Faraday wave driven turbulence reveal a transition from weakly dispersing superdiffusive regime to strongly dispersing Brownian diffusion as the flow energy is increased in a broad range. The transition to fully developed 2D turbulence is characterized by the topological changes in the fluid particle trajectories and the development of self-similar diffusion. The degree of 2D turbulence development can be quantified by a parameter describing the deviation of single particle dispersion from the Taylor dispersion.

We theoretically and experimentally investigate high-harmonic generation in a 78-MHz enhancement cavity with a transverse mode having on-axis intensity maxima at the focus and minima at an opening in the following mirror. We find that the conversion efficiency is comparable to that achievable with a Gaussian mode, whereas the output coupling efficiency can be significantly improved over any other demonstrated technique. This approach offers additional power scaling advantages and additional degrees of freedom in shaping the harmonic emission, paving the way to high-power extreme-ultraviolet frequency combs and the generation of multi-MHz repetition-rate-isolated attosecond pulses.

Our numerical simulations of tidal flow of a stratified fluid over periodic knife-edge ridges and random topography reveal that the time-averaged tidal energy converted into internal gravity wave radiation arises only from the section of a ridge above a virtual seafloor. The average radiated power is approximated by the power predicted by linear theory if the height of the ridge is measured relative to the virtual floor. The concept of a virtual floor can extend the applicability of linear theory to global predictions of the conversion of tidal energy into internal wave energy in the oceans.

Localized structures have been observed in many spatially extended systems of either biological, chemical, or physical nature. Here, we study experimentally front pinning and dissipative localized structures in a delayed optical system based on a bistable semiconductor laser with optoelectronic feedback. We observe that many of the concepts known to apply to spatially localized structures also apply in this context, with specificities related to the lack of reversibility symmetry. Numerical simulations based on purely prototypical modeling reproduce very well the experimental findings, which indicates that the results do not depend on the specific physical system under consideration, but are, on the contrary, very generic features of time delayed systems.

A series of experiments is performed to examine the arrival of a pulse peak, using a Gaussian-shaped temporal wave packet as the input pulse and truncating it at various positions on or before the peak of the packet. When the truncating point is within the negative group delay limit of the fast light medium, a smooth Gaussian peak is observed at the exit port, despite the absence of an input pulse peak. The experimental results explicitly demonstrate that the superluminal propagation of a smooth Gaussian-shaped pulse peak is an analytic continuation over time of the earlier portion of the input pulse envelope. To investigate the physical meaning of the pulse peak further, we also examine the propagation of triangular-shaped pulses, for which the pulse peak can be recognized as a nonanalytical point.

We report the experimental observation of a submicron cellular structure on the surface of silicon targets eroded by an ion plasma. Analysis by atomic force microscopy allows us to assess the time evolution and show that the system can be described quantitatively by the convective Cahn-Hilliard equation, found in the study of domain coarsening for a large class of driven systems. The space-filling trait of the ensuing pattern relates it to evolving foams. Through this connection, we are actually able to derive the coarsening law for the pattern wavelength from the nontrivial topological dynamics of the cellular structure. Thus, the study of the topological properties of patterns in nonvariational spatially extended systems emerges as complementary to morphological approaches to their challenging coarsening properties.

We investigate wrinkling of two-dimensional random and triangular semiflexible polymer networks under shear. Both types of semiflexible networks exhibit wrinkling above a small critical shear angle, which scales with an exponent of the bending modulus between 1.9 and 2.0. Random networks exhibit hysteresis at the wrinkling threshold. Wrinkling lowers the total elastic energy by up to 20% and strongly affects the elastic properties of all semiflexible networks such as the crossover between bending and stretching dominated behavior. In random networks, we also find evidence for metastable wrinkled configurations. While the disordered microstructure of random networks affects the scaling behavior of wrinkle amplitudes, it has little effect on wrinkle wavelength. Therefore, wrinkles represent a robust, microstructure-independent assay of shear strain or elastic properties.

High quality factor whispering-gallery-mode microresonators are ideally suited for nonlinear optical interactions. We analyze, experimentally and theoretically, a variety of ${\chi }^{(3)}$ nonlinear interactions in silica microspheres, consisting of third harmonic generation and Raman assisted third order sum-frequency generation in the visible. A tunable, room temperature, cw multicolor emission in silica microspherical whispering-gallery-mode microresonators has been achieved by controlling the cavity mode dispersion and exciting nonequatorial modes for efficient frequency conversion.

We observe a strong variation of the Zeeman splitting of exciton polaritons in microcavities when switching between the linear regime, the polariton lasing, and photon lasing regimes. In the polariton lasing regime the sign of Zeeman splitting changes compared to the linear regime, while in the photon lasing regime the splitting vanishes. We additionally observe an increase of the diamagnetic shift in the polariton lasing regime. These effects are explained in terms of the nonequilibrium “spin Meissner effect.”

Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantum-mechanical scenario possible, i.e., a quantum-mechanical self-sustained oscillator coupled to an external harmonic drive. Using the power spectrum we analyze synchronization in terms of frequency entrainment and frequency locking in close analogy to the classical case. We show that there is a steplike crossover to a synchronized state as a function of the driving strength. In contrast to the classical case, there is a finite threshold value in driving. Quantum noise reduces the synchronized region and leads to a deviation from strict frequency locking.

The formation of localized periodic structures in the deformation of elastic shells is well documented and is a familiar first stage in the crushing of a spherical shell such as a ping-pong ball. While spherical shells manifest such periodic structures as polygons, we present a new instability that is observed in the indentation of a highly ellipsoidal shell by a horizontal plate. Above a critical indentation depth, the plate loses contact with the shell in a series of well-defined “blisters” along the long axis of the ellipsoid. We characterize the onset of this instability and explain it using scaling arguments, numerical simulations, and experiments. We also characterize the properties of the blistering pattern by showing how the number of blisters and their size depend on both the geometrical properties of the shell and the indentation but not on the shell’s elastic modulus. This blistering instability may be used to determine the thickness of highly ellipsoidal shells simply by squashing them between two plates.

Aging is a familiar phenomenon from glassy systems like spin glasses and materials with slow relaxation processes, breaking of time-translation invariance, and dynamical scaling. We study aging in active rotators and Kuramoto oscillators that are coupled with frustrated bonds. The induced multiplicity of attractors of fixed-point or limit-cycle solutions leads to a rough potential landscape. When the system is exposed to noise, the oscillator phases migrate through this landscape and generate a multitude of different escape times from one metastable state to the next. When the system is quenched from the regime of a unique fixed point toward the regime of multistable limit-cycle solutions, the autocorrelation functions depend on the waiting time after the quench and show dynamical scaling. In this way we uncover a common mechanism behind aging in quite different realizations.

We report on the multicontact frictional dynamics of model elastomer surfaces rubbed against bare glass slides. The surfaces consist of layers patterned with thousands of spherical caps distributed both spatially and in height, regularly or randomly. Use of spherical asperities yields circular microcontacts whose radii are a direct measure of the contact pressure distribution. Optical tracking of individual contacts provides the in-plane deformations of the tangentially loaded interface, yielding the shear force distribution. We then investigate the stick-slip frictional dynamics of a regular hexagonal array. For all stick phases, slip precursors are evidenced and found to propagate quasistatically, normally to the isopressure contours. A simple quasistatic model relying on the existence of interfacial stress gradients is derived and predicts qualitatively the position of slip precursors.

We propose a method to control electromagnetic flux in an almost arbitrary way in wavelength and subwavelength scales. The capability of subwavelength flux control is enabled by the evanescent waves induced in a class of inhomogeneous anisotropic media with a near-zero permittivity component. By designing the spatial profile of the other permittivity component in such inhomogeneous media, the flow and distribution of energy flux can be conveniently manipulated. This method provides another approach to efficiently control electromagnetic flux in nonmagnetic media.

Phase transition in its strict sense can only be observed in an infinite system, for which equilibration takes an infinitely long time at criticality. In numerical simulations, we are often limited both by the finiteness of the system size and by the finiteness of the observation time scale. We propose that one can overcome this barrier by measuring the nonequilibrium temporal relaxation for finite systems and by applying the finite-time–finite-size scaling (FTFSS) which systematically uses two scaling variables, one temporal and the other spatial. The FTFSS method yields a smooth scaling surface, and the conventional finite-size scaling curves can be viewed as proper cross sections of the surface. The validity of our FTFSS method is tested for the synchronization transition of Kuramoto models in the globally coupled structure and in the small-world network structure. Our FTFSS method is also applied to the Monte Carlo dynamics of the globally coupled $q$-state clock model.

We consider a low-dimensional model of convection in a horizontally magnetized layer of a viscous fluid heated from below. We analyze in detail the stability of hydrodynamic convection for a wide range of two control parameters. Namely, when changing the initially applied temperature difference or magnetic field strength, one can see transitions from regular to irregular long-term behavior of the system, switching between chaotic, periodic, and equilibrium asymptotic solutions. It is worth noting that owing to the induced magnetic field a transition to hyperchaotic dynamics is possible for some parameters of the model. We also reveal new features of the generalized Lorenz model, including both type I and III intermittency.

The semiclassical and quantum dynamics of two ultrastrongly coupled nonlinear resonators cannot be explained using the discrete nonlinear Schrödinger equation or the Bose-Hubbard model, respectively. Instead, a model beyond the rotating wave approximation must be studied. In the semiclassical limit this model is not integrable and becomes chaotic for a finite window of parameters. For the quantum dimer we find corresponding regions of stability and chaos. The more striking consequence for both semiclassical and quantum chaos is that the tunneling time between the sites becomes unpredictable. These results, including the transition to chaos, can be tested in experiments with superconducting microwave resonators.