We study the mechanical response of elastic rods bent into open knots, focusing on the case of trefoil and cinquefoil topologies. The limit of a weak applied tensile force is studied both analytically and experimentally: the Kirchhoff equations with self-contact are solved by means of matched asymptotic expansions; predictions on both the geometrical and mechanical properties of the elastic equilibrium are compared to experiments. The extension of the theory to tight knots is discussed.

Using a numerical technique we demonstrate that the flow of the simplest differential viscoelastic fluid model (i.e., the upper-convected Maxwell model) goes through a bifurcation to a steady asymmetric state when flowing in a perfectly symmetric “cross-slot” geometry. We show that this asymmetry is purely elastic in nature and that the effect of inertia is a stabilizing one. Our results are in qualitative agreement with very recent experimental visualizations of a similar flow in the microfluidic apparatus of Arratia et al. [Phys. Rev. Lett. 96, 144502 (2006)].

Lyapunov instability of a “diatomic” system of coupled map lattices is studied and the dynamics of Lyapunov modes (LMs) is compared with phonon dynamics. Similar to the phonon case mass differences between neighboring sites induce gaps in the Lyapunov spectrum and LMs split into two types correspondingly. An unexpected finding is that contrary to the phonon case a nontrivial threshold value for the mass difference is required for the occurrence of the spectral gap and the splitting of LMs. A possible origin of such a nontrivial threshold value of mass differences is suggested.

By performing two parallel numerical experiments—solving the dynamical Hamiltonian equations and solving the Hasselmann kinetic equation—we examined the applicability of the theory of weak turbulence to the description of the time evolution of an ensemble of free surface waves (a swell) on deep water. We observed qualitative coincidence of the results. To achieve quantitative coincidence, we augmented the kinetic equation by an empirical dissipation term modeling the strongly nonlinear process of white capping. Fitting the two experiments, we determined the dissipation function due to wave breaking and found that it depends very sharply on the parameter of nonlinearity (the surface steepness). The onset of white capping can be compared to a second-order phase transition. The results corroborate the experimental observations of Banner, Babanin, and Young [J. Phys. Oceanogr. 30, 3145 (2000)].

The first direct experimental evidence of the suppression of quasi-two-dimensional turbulence by mean flows is presented. The flow either is induced externally or appears in the process of spectral condensation due to an inverse cascade in bounded turbulence. The observed suppression of large scales is consistent with an expected reduction in the correlation time of turbulent eddies due to shearing. At high flow velocities, sweeping of the forcing-scale vortices reduces the energy input, leading to a reduction in the turbulence level.

We present the first study of subwavelength discrete solitons in nonlinear metamaterials: nanoscaled periodic structures consisting of metal and nonlinear dielectric slabs. The solitons supported by such media result from a balance between tunneling of surface plasmon modes and nonlinear self-trapping. The dynamics in such systems, arising from the threefold interplay between periodicity, nonlinearity, and surface plasmon polaritons, is substantially different from that in conventional nonlinear dielectric waveguide arrays. We expect these phenomena to inspire fundamental studies as well as potential applications of nonlinear metamaterials, particularly in subwavelength nonlinear optics.

Two-dimensional fronts and coarsening dynamics with a $t^{1/2}$ power law are analyzed experimentally and theoretically in a nonlinear optical system of a sodium vapor cell with single-mirror feedback. Modifications of the $t^{1/2}$ power law are observed in the vicinity of a modulational instability leading to the formation of spatial solitons of different sizes. The experimental and numerical observations give direct evidence for the locking of fronts as the mechanism of soliton formation. A phenomenological equation for the dynamics of the domain radius explains the observed behavior.

We investigate the effects of two-dimensional confinement on the lasing properties of a classical random laser system operating in the incoherent feedback (diffusive) regime. A suspension of 250 nm rutile (${\mathrm{TiO}}_2$) particles in a rhodamine 6G solution was inserted into the hollow core of a photonic crystal fiber generating the first random fiber laser and a novel quasi-one-dimensional random laser geometry. A comparison with similar systems in bulk format shows that the random fiber laser presents an efficiency that is at least 2 orders of magnitude higher.

Chaotic systems share with stochastic processes several properties that make them almost undistinguishable. In this communication we introduce a representation space, to be called the complexity-entropy causality plane. Its horizontal and vertical axis are suitable functionals of the pertinent probability distribution, namely, the entropy of the system and an appropriate statistical complexity measure, respectively. These two functionals are evaluated using the Bandt-Pompe recipe to assign a probability distribution function to the time series generated by the system. Several well-known model-generated time series, usually regarded as being of either stochastic or chaotic nature, are analyzed so as to illustrate the approach. The main achievement of this communication is the possibility of clearly distinguishing between them in our representation space, something that is rather difficult otherwise.

The sine-Gordon model with a variable mass (VMSG) appears in many physical systems, ranging from the current through a nonuniform Josephson junction to DNA-promoter dynamics. Such models are usually nonintegrable with solutions found numerically or perturbatively. We construct a class of VMSG models, integrable at both the classical and the quantum levels with exact soliton solutions, which can accelerate and change their shape, width, and amplitude simulating realistic inhomogeneous systems at certain limits.

A rope falling onto a solid surface typically forms a series of regular coils. Here, we study this phenomenon using laboratory experiments (with cotton threads and softened spaghetti) and an asymptotic “slender-rope” numerical model. The excellent agreement between the two with no adjustable parameters allows us to determine a complete phase diagram for elastic coiling comprising three basic regimes involving different force balances (elastic, gravitational, and inertial) together with resonant “whirling string” and “whirling shaft” eigenmodes in the inertial regime.

Using heat conduction mechanism on a social network we develop a systematic method to predict missing values as recommendations. This method can treat very large matrices that are typical of internet communities. In particular, with an innovative, exact formulation that accommodates arbitrary boundary condition, our method is easy to use in real applications. The performance is assessed by comparing with traditional recommendation methods using real data.

We report on what is, to our knowledge, the first cw pumped Raman fiber-gas laser based on a hollow-core photonic crystal fiber filled with hydrogen. The high efficiency of the gas-laser interaction inside the fiber allows operation in a single-pass configuration. The transmitted spectrum exhibits 99.99% of the output light at the Stokes wavelength and a pump power threshold as low as 2.25 W. The study of the Stokes emission evolution with pressure shows that highly efficient Raman amplification is still possible even at atmospheric pressure. The addition of fiber Bragg gratings to the system, creating a cavity at the Stokes wavelength, reduces the Raman threshold power below 600 mW.

A flexibly mounted circular cylinder in cross-flow, with natural frequencies in the inline and transverse directions having a ratio close to $2:1$, exhibits drastic changes in the vortex structures in its wake, the frequency content of the fluid forces, and the orbital shape of its resulting motions. Stable multivortex patterns form in the cylinder wake, associated with large high-frequency force components.

We inquire into the scaling properties of the 2D Navier-Stokes equation sustained by a force field with Gaussian statistics, white noise in time, and with a power-law correlation in momentum space of degree $2-2\epsilon$. This is at variance with the setting usually assumed to derive Kraichnan’s classical theory. We contrast accurate numerical experiments with the different predictions provided for the small $\epsilon$ regime by Kraichnan’s double cascade theory and by renormalization group analysis. We give clear evidence that for all $\epsilon$, Kraichnan’s theory is consistent with the observed phenomenology. Our results call for a revision in the renormalization group analysis of (2D) fully developed turbulence.

We report an experimental study of liquid drops moving against gravity, when placed on a vertically vibrating inclined plate, which is partially wetted by the drop. The frequency of vibrations ranges from 30 to 200 Hz, and, above a threshold in vibration acceleration, drops experience an upward motion. We attribute this surprising motion to the deformations of the drop, as a consequence of an up or down symmetry breaking induced by the presence of the substrate. We relate the direction of motion to contact angle measurements. This phenomenon can be used to move a drop along an arbitrary path in a plane, without special surface treatments or localized forcing.

We study the propagation of light through randomly packed films of micron-sized spheres. Dried films consist of strongly scattering core-shell particles mixed with polymer spheres, which are then dissolved to tune the number of contacts, $Z$, among the remaining scatterers. The transport mean free path $l^{*}$ is measured from the width of the coherent backscattering cone; $l^{*}=2.1\mu \mathrm{m}$ when $Z\sim 4–5$, but increases twofold (scattering weakens) in a film with $Z\sim 9–10$. The results contradict the standard diffusive transport model, but are explained by accounting for optical coupling of contacting spheres.

Selective enhancement ($>{10}^3$) of harmonics extending to the water window ($\sim 4\mathrm{nm}$) generated in an argon gas filled straight bore capillary waveguide is demonstrated. This enhancement is in good agreement with modeling which indicates that multimode quasi-phase-matching is achieved by rapid axial intensity modulations caused by beating between the fundamental and higher-order capillary modes. Substantial pulse energies ($>10\mathrm{nJ}$ per pulse per harmonic order) at wavelengths beyond the carbon $K$ edge ($\sim 4.37\mathrm{nm}$, $\sim 284\mathrm{eV}$) up to $\sim 360\mathrm{eV}$ are observed from argon ions for the first time.

We investigate the spatial dynamics of optical necklace beams in Kerr media. For powers corresponding to less than the critical power for self-focusing per bead, we experimentally confirm the confinement of these necklace beams as proposed in [Phys. Rev. Lett. 81, 4851 (1998)]. At higher powers, we observe a transition from collective necklace behavior to one in which the beads of the necklace collapse independently. We observe that, below the transition power, the perturbed necklace still behaves in a collective manner with coupling between individual beads but that, at higher powers, it undergoes a similar transition to a decoupled state of the necklace.

We propose a general chemotactic model describing a system of interacting elements. Each element in this model exhibits internal dynamics, and there exists a nonlinear coupling between elements that depends on their internal states. From this model, we derive a simpler model describing the phases and positions of the chemotactic elements by means of center-manifold and phase-reduction methods. We find that, despite its simplicity, the model obtained through this reduction exhibits a rich variety of patterns.