All physical systems are affected by some noise that limits the resolution that can be attained in partitioning their state space. For chaotic, locally hyperbolic flows, this resolution depends on the interplay of the local stretching or contraction and the smearing due to noise. We propose to determine the “finest attainable” partition for a given hyperbolic dynamical system and a given weak additive white noise, by computing the local eigenfunctions of the adjoint Fokker-Planck operator along each periodic point, and using overlaps of their widths as the criterion for an optimal partition. The Fokker-Planck evolution is then represented by a finite transition graph, whose spectral determinant yields time averages of dynamical observables. Numerical tests of such “optimal partition” of a one-dimensional repeller support our hypothesis.

Multiwalled carbon nanotubes (MWCNT) are exposed to a transient and strong liquid jet flow created by a pair of differently sized laser-induced cavitation bubbles. The position and size of the bubbles are controlled with a spatial light modulator within a $15\mu \mathrm{m}$ thick liquid gap. Depending on the tube’s position with respect to this jet flow, rotation, translation, and a bending deformation is observed with a high-speed camera recording at up to 300 000 frames per second. By measuring the decay time of the respective bending modes we determine the flexural rigidity of MWCNTs to be on the range of $0.45–4.06\times {10}^{-19}\mathrm{N}{\mathrm{m}}^2$. The average diameter of the MWCNTs is $117.8\pm 6.7\mathrm{nm}$ with a thickness of $4.6\pm 0.75\mathrm{nm}$, yielding a Young’s modulus between 0.033–0.292 TPa.

X-ray tomography is performed to acquire 3D images of crumpled aluminum foils. We develop an algorithm to trace out the labyrinthian paths in the three perpendicular cross sections of the data matrices. The tangent-tangent correlation function along each path is found to decay exponentially with an effective persistence length that shortens as the crumpled ball becomes more compact. In the meantime, we observed ordered domains near the crust, similar to the lamellae phase mixed by the amorphous portion in lyotropic liquid crystals. The size and density of these domains grow with further compaction, and their orientation favors either perpendicular or parallel to the radial direction. Ordering is also identified near the core with an arbitrary orientation, exemplary of the spontaneous symmetry breaking.

We report a direct determination of the specular scattering probability of acoustic phonons at a crystal boundary by observing the escape of incident coherent phonons from the coherent state during reflection. In the sub-THz frequency range where the phonon wavelength is much longer than the lattice constant, the acoustic phonon-interface interaction is found to agree well with the macroscopic theory on wave scattering from rough surfaces. This examination thus quantitatively verifies the dominant role of atomic-scale corrugations in the Kapitza anomaly observed at 1–10 K and further opens a new path to nondestructively estimate subnanoscale roughness of buried interfaces.

We study the strong coupling of light and nanoparticle suspensions and their surface tension effect in capillaries. We show experimentally and theoretically that increasing the intensity of a narrow laser beam passing through a capillary far away from the surface results in a significant decrease in the fluid level. The underlying mechanism relies on light-induced redistribution of nanoparticles in the bulk and the surface of the fluid, facilitating continuous optical control over the surface position. The experiments manifest optical control from afar over properties of fluid surfaces.

It has been shown experimentally over nearly 80 years that surface fine roughness of circular pipes has a crucial effect on the natural transition to turbulence. In this Letter, a theoretical explanation is suggested for the roughness-induced instability. Once the nonlinear effect of roughness is introduced (through a pipe with fine corrugation surface), the mean velocity profile becomes unstable to three-dimensional, asymmetric, and helical traveling waves at moderate Reynolds numbers. The threshold of the aspect ratio or shape factor of the roughness element required to cause instability scales as ${\mathrm{Re}}^{-2}$. Inspired by the current model, a scaling form is proposed and the scaled friction factor measurements in rough pipes collapse onto a universal curve.

It is shown experimentally that surfactants can change the thinning rate of fluid necks undergoing rupture. In the case of two-fluid pinch-off, two or three linear regimes are observed for the variation of the neck radius versus time. The surface tension in the neck region changes with time, as a result of surfactant depletion. Similar results are obtained for the case of a single fluid pinching in air. The depletion of surfactant can be either partial or complete depending on the rate of transport of the surfactant from the bulk to the surface.

We propose and analyze the “complementary” structure of a metallic nanogap, namely, the metallic nanowire for magnetic field enhancement. A huge enhancement of the field up to a factor of 300 was achieved. Introducing the surface impedance concept, we also develop and numerically confirm a new analytic theory which successfully predicts the field enhancement factors for metal nanostructures. Compared to the predictions of the classical Babinet principle applied to a nanogap, an order of magnitude difference in the field enhancement factor was observed for the sub-skin-depth regime nanowire.

We discover a strong localization of flexural (bi-Laplacian) waves in rigid thin plates. We show that clamping just one point inside such a plate not only perturbs its spectral properties, but essentially divides the plate into two independently vibrating regions. This effect progressively appears when increasing the plate eccentricity. Such a localization is qualitatively and quantitatively different from the results known for the Laplacian waves in domains of irregular boundary. It would allow us to control the confinement of mechanical vibrations in rigid plates and of eddies in the slow Stokes flow.

The measured spatial coherence characteristics of the illumination used in a diffractive imaging experiment are incorporated in an algorithm that reconstructs the complex transmission function of an object from experimental x-ray diffraction data using 1.4 keV x rays. Conventional coherent diffractive imaging, which assumes full spatial coherence, is a limiting case of our approach. Even in cases in which the deviation from full spatial coherence is small, we demonstrate a significant improvement in the quality of wave field reconstructions. Our formulation is applicable to x-ray and electron diffraction imaging techniques provided that the spatial coherence properties of the illumination are known or can be measured.

A perfect invisibility cloak is commonly believed to be undetectable from electromagnetic (EM) detection because it is equivalent to a curved but empty EM space created from coordinate transformation. Based on the intrinsic asymmetry of coordinate transformation applied to motions of photons and charges, we propose a method to detect this curved EM space by shooting a fast-moving charged particle through it. A broadband radiation generated in this process makes a cloak visible. Our method is the only known EM mechanism so far to detect an ideal perfect cloak (curved EM space) within its working band.

Interactions of nanoscale structures with fluids are of current interest both in the elucidation of fluid dynamics at these small scales, and in determining the ultimate performance of nanoelectromechanical systems outside of vacuum. We present a comprehensive study of nanomechanical damping in three gases (He, ${\mathrm{N}}_2$, ${\mathrm{CO}}_2$), and liquid ${\mathrm{CO}}_2$. Resonant dynamics in multiple devices of varying size and frequency is measured over 10 decades of pressure (1 mPa–20 MPa) using time-domain stroboscopic optical interferometry. The wide pressure range allows full exploration of the regions of validity of Newtonian and non-Newtonian flow damping models. Observing free molecular flow behavior extending above 1 atm, we find a fluid relaxation time model to be valid throughout, but not beyond, the non-Newtonian regime, and a Newtonian flow vibrating spheres model to be valid in the viscous limit.

We present a study of the propagation of higher-order spatial modes in a waveguided parametric down-conversion photon-pair source. Observing the multimode photon-pair spectrum from a periodically poled $\mathrm{KTiOP}{\mathrm{O}}_4$ waveguide allowed us to isolate individual spatial modes through their distinctive spectral properties. We have measured directly the spatial distribution of each mode of the photon pairs, confirming the findings of our waveguide model, and demonstrated by coincidence measurements that the total parity of the modes is conserved in the nonlinear interaction. Furthermore, we show that we can combine the advantages of a waveguide source with the potential to generate spatially entangled photon pairs as in bulk-crystal down-converters.

We analyze the coherent-structure interaction and the formation of bound states in active dispersive-dissipative nonlinear media using a viscous film coating a vertical fiber as a prototype. The coherent structures in this case are droplike pulses that dominate the evolution of the film. We study experimentally the interaction dynamics and show evidence for formation of bound states. A theoretical explanation is provided through a coherent-structures theory of a simple model for the flow.

In a thin, dilute, and fast flowing granular layer, the impact of a small sphere generates a fast growing hole devoid of matter. The growth of this hole is studied in detail, and its dynamics is found to mimic that of blast shocks in gases. This dynamics can be decomposed into two stages: a fast initial stage (the blast) and a slower growth regime whose growth velocity is given by the speed of sound in the medium used. A simple model using ingredients already invoked for the case of blast shocks in gases but including the inelastic nature of collisions between grains accounts accurately for our results. The system studied here allows for a detailed study of the full dynamics of a blast as it relaxes from a strong to a weak shock and later to an acoustic disturbance.

We demonstrate spectrally tuned dispersive and reactive optical force in a cavity optomechanics system that comprises a microdisk and a vibrating nanomechanical beam waveguide. The waveguide coupled to the microdisk acts as a bosonic dissipation channel and its motion modulates the cavity’s damping rate. As a result a reactive optical force arises in addition to the normal dispersive force. The cavity enhanced force is not observed at zero detuning but shows asymmetric behavior with a maximum at red-detuned offset. Such reactive cavity backaction force points to new avenues in cavity optomechanics.

We study the breathing mode in systems of trapped interacting particles. Our approach, based on a dynamical ansatz in the first equation of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy allows us to tackle at once a wide range of power-law interactions and interaction strengths, at linear and nonlinear levels. This both puts in a common framework various results scattered in the literature, and by widely generalizing these, emphasizes universal characters of this breathing mode. Our findings are supported by direct numerical simulations.

We present experimental observations of strong electric and magnetic interactions between split ring resonators (SRRs) in metamaterials. We fabricated near-infrared planar metamaterials with different inter-SRR spacings along different directions. Our transmission measurements show blueshifts and redshifts of the magnetic resonance, depending on SRR orientation relative to the lattice. The shifts agree well with simultaneous magnetic and electric near-field dipole coupling. We also find large broadening of the resonance, accompanied by a decrease in effective cross section per SRR with increasing density due to superradiant scattering. Our data shed new light on Lorentz-Lorenz approaches to metamaterials.

Identifying temporally invariant components in complex multivariate time series is key to understanding the underlying dynamical system and predict its future behavior. In this Letter, we propose a novel technique, stationary subspace analysis (SSA), that decomposes a multivariate time series into its stationary and nonstationary part. The method is based on two assumptions: (a) the observed signals are linear superpositions of stationary and nonstationary sources; and (b) the nonstationarity is measurable in the first two moments. We characterize theoretical and practical properties of SSA and study it in simulations and cortical signals measured by electroencephalography. Here, SSA succeeds in finding stationary components that lead to a significantly improved prediction accuracy and meaningful topographic maps which contribute to a better understanding of the underlying nonstationary brain processes.

The nonlinear wave pattern generated by a localized pressure source moving over a liquid free surface at speeds below the minimum phase speed ($c_{\min }$) of linear gravity-capillary waves is investigated experimentally and theoretically. At these speeds, freely propagating fully localized solitary waves, or “lumps,” are known theoretically to be possible. For pressure-source speeds far below $c_{\min }$, the surface response is a local depression similar to the case with no forward speed. As the speed is increased, a critical value is reached $c_c\approx 0.9c_{\min }$ where there is an abrupt transition to a wavelike state that features a steady disturbance similar to a steep lump behind the pressure forcing. As the speed approaches $c_{\min }$, a second transition is found; the new state is unsteady and is characterized by continuous shedding of lumps from the tips of a $\mathsf{V}$-shaped pattern.