In situ 3D reconfigurable ultrasonically sculpted optical beam paths.

We demonstrate that optical beams can be spatially and temporally shaped in situ by forming 3D reconfigurable interference patterns of ultrasound waves in the medium. In this technique, ultrasonic pressure waves induce a modulated refractive index pattern that shapes the optical beam as it propagates through the medium. Using custom-designed cylindrical ultrasonic arrays, we demonstrate that complex patterns of light can be sculpted in the medium, including dipole and quadrupole shapes. Additionally, through a combination of theory and experiment, we demonstrate that these optical patterns can be scanned in radial and azimuthal directions. Moreover, we show that light can be selectively confined to different extrema of the spatial ultrasound pressure profile by temporally synchronizing lightwave and ultrasound. Finally, we demonstrate that this technique can also be used to define spatial patterns of light in turbid media. The notion of in situ 3D sculpting of optical beam paths using ultrasound interference patterns can find intriguing applications in biological imaging and manipulation, holography, and microscopy.

Broadband cloaking in stratified seas.

Here we show that floating objects in stratified fluids can be cloaked against broadband incident waves by properly architecting the bottom corrugations. The presented invisibility cloaking of gravity waves is achieved utilizing a nonlinear resonance concept that occurs between surface and internal waves mediated by the bottom topography. Our cloak bends wave rays from the surface into the body of the fluid. Wave rays then pass underneath the floating object and may be recovered back to the free surface at the downstream bearing no trace of diffraction or scattering. The cloak is the proper architecture of bottom corrugations only, and hence is surface noninvasive. The presented scheme is a nonlinear alternative to the transformation-based cloaking, but in the context of dispersive waves.

Frequency-dependent higher-order Stokes singularities near a planar elastic boundary: Implications for the hydrodynamics of an active microswimmer near an elastic interface.

The emerging field of self-driven active particles in fluid environments has recently created significant interest in the biophysics and bioengineering communities owing to their promising future for biomedical and technological applications. These microswimmers move autonomously through aqueous media, where under realistic situations they encounter a plethora of external stimuli and confining surfaces with peculiar elastic properties. Based on a far-field hydrodynamic model, we present an analytical theory to describe the physical interaction and hydrodynamic couplings between a self-propelled active microswimmer and an elastic interface that features resistance toward shear and bending. We model the active agent as a superposition of higher-order Stokes singularities and elucidate the associated translational and rotational velocities induced by the nearby elastic boundary. Our results show that the velocities can be decomposed in shear and bending related contributions which approach the velocities of active agents close to a no-slip rigid wall in the steady limit. The transient dynamics predict that contributions to the velocities of the microswimmer due to bending resistance are generally more pronounced than those due to shear resistance. Bending can enhance (suppress) the velocities resulting from higher-order singularities whereas the shear related contribution decreases (increases) the velocities. Most prominently, we find that near an elastic interface of only energetic resistance toward shear deformation, such as that of an elastic capsule designed for drug delivery, a swimming bacterium undergoes rotation of the same sense as observed near a no-slip wall. In contrast to that, near an interface of only energetic resistance toward bending, such as that of a fluid vesicle or liposome, we find a reversed sense of rotation. Our results provide insight into the control and guidance of artificial and synthetic self-propelling active microswimmers near elastic confinements.

Ultrasonic sculpting of virtual optical waveguides in tissue.

Optical imaging and stimulation are widely used to study biological events. However, scattering processes limit the depth to which externally focused light can penetrate tissue. Optical fibers and waveguides are commonly inserted into tissue when delivering light deeper than a few millimeters. This approach, however, introduces complications arising from tissue damage. In addition, it makes it difficult to steer light. Here, we demonstrate that ultrasound can be used to define and steer the trajectory of light within scattering media by exploiting local pressure differences created by acoustic waves that result in refractive index contrasts. We show that virtual light pipes can be created deep into the tissue (>18 scattering mean free paths). We demonstrate the application of this technology in confining light through mouse brain tissue. This technology is likely extendable to form arbitrary light patterns within tissue, extending both the reach and the flexibility of light-based methods.

Flow characteristics of Chlamydomonas result in purely hydrodynamic scattering.

It has long been believed that eukaryotic flagellated swimming cells feel solid boundaries through direct ciliary contact. Specifically, based on observations of behavior of green alga Chlamydomonas reinhardtii it has been reported that it is their "flagella [that] prevent the cell body from touching the surface" [Kantsler et al., Proc. Natl. Acad. Sci. USA 110, 1187 (2013)PNASA60027-842410.1073/pnas.1210548110]. Here, via investigation of a model swimmer whose flow field closely resembles that of C. reinhardtii, we show that the scattering from a wall can be purely hydrodynamic and that no mechanical or flagellar force is needed for sensing and escaping the boundary.

Hydrodynamic Choreographies of Microswimmers.

We unveil orbital topologies of two nearby swimming microorganisms using an artificial microswimmer, called Quadroar. Depending on the initial conditions of the microswimmers, we find diverse families of attractors including dynamical equilibria, bound orbits, braids, and pursuit-evasion games. We also observe a hydrodynamic slingshot effect: a system of two hydrodynamically interacting swimmers moving along braids can advance in space faster than non-interacting swimmers that have the same actuation parameters and initial conditions as the interacting ones. Our findings suggest the existence of complex collective behaviors of microswimmers, from equilibrium to rapidly streaming states.

Broadband Bending of Flexural Waves: Acoustic Shapes and Patterns.

Directing and controlling flexural waves in thin plates along a curved trajectory over a broad frequency range is a significant challenge that has various applications in imaging, cloaking, wave focusing, and wireless power transfer circumventing obstacles. To date, all studies appeared controlling elastic waves in structures using periodic arrays of inclusions where these structures are narrowband either because scattering is efficient over a small frequency range, or the arrangements exploit Bragg scattering bandgaps, which themselves are narrowband. Here, we design and experimentally test a wave-bending structure in a thin plate by smoothly varying the plate's rigidity (and thus its phase velocity). The proposed structures are (i) broadband, since the approach is frequency-independent and does not require bandgaps, and (ii) capable of bending elastic waves along convex trajectories with an arbitrary curvature.

Broadband cloaking of flexural waves.

The governing equation for elastic waves in flexural plates is not form invariant, and hence designing a cloak for such waves faces a major challenge. Here, we present the design of a perfect broadband cloak for flexural waves through the use of a nonlinear transformation in the region of the cloak and by matching term by term the original and transformed equations and also assuming a prestressed material with body forces. For a readily achievable flexural cloak in a physical setting, we further present an approximate adoption of our perfect cloak under more restrictive physical constraints. Through direct simulation of the governing equations, we show that this cloak, as well, maintains a consistently high cloaking efficiency over a broad range of frequencies. The methodology developed here may be used for steering waves and designing cloaks in other physical systems with non-form-invariant governing equations.

Suppression of epileptic seizures via Anderson localization.

Here we show that brain seizures can be effectively suppressed through random modulation of the brain medium. We use an established mesoscale cortical model in the form of a system of coupled stochastic partial differential equations. We show that by temporal and spatial randomization of parameters governing the firing rates of the excitatory and inhibitory neuron populations, seizure waves can be significantly suppressed. We find that the attenuation is the most effective when applied to the mean threshold potential. The proposed technique can serve as a non-invasive paradigm to mitigate epileptic seizures without knowing the location of the epileptic foci.

Terminal retrograde turn of rolling rings.

We report an unexpected reverse spiral turn in the final stage of the motion of rolling rings. It is well known that spinning disks rotate in the same direction of their initial spin until they stop. While a spinning ring starts its motion with a kinematics similar to disks, i.e., moving along a cycloidal path prograde with the direction of its rigid body rotation, the mean trajectory of its center of mass later develops an inflection point so that the ring makes a spiral turn and revolves in a retrograde direction around a new center. Using high speed imaging and numerical simulations of models featuring a rolling rigid body, we show that the hollow geometry of a ring tunes the rotational air drag resistance so that the frictional force at the contact point with the ground changes its direction at the inflection point and puts the ring on a retrograde spiral trajectory. Our findings have potential applications in designing topologically new surface-effect flying objects capable of performing complex reorientation and translational maneuvers.

Fabry-Perot resonance of water waves.

We show that significant water wave amplification is obtained in a water resonator consisting of two spatially separated patches of small-amplitude sinusoidal corrugations on an otherwise flat seabed. The corrugations reflect the incident waves according to the so-called Bragg reflection mechanism, and the distance between the two sets controls whether the trapped reflected waves experience constructive or destructive interference within the resonator. The resulting amplification or suppression is enhanced with increasing number of ripples and is most effective for specific resonator lengths and at the Bragg frequency, which is determined by the corrugation period. Our analysis draws on the analogous mechanism that occurs between two partially reflecting mirrors in optics, a phenomenon named after its discoverers Charles Fabry and Alfred Perot.

The evolution of air resonance power efficiency in the violin and its ancestors.

The fact that acoustic radiation from a violin at air-cavity resonance is monopolar and can be determined by pure volume change is used to help explain related aspects of violin design evolution. By determining the acoustic conductance of arbitrarily shaped sound holes, it is found that air flow at the perimeter rather than the broader sound-hole area dominates acoustic conductance, and coupling between compressible air within the violin and its elastic structure lowers the Helmholtz resonance frequency from that found for a corresponding rigid instrument by roughly a semitone. As a result of the former, it is found that as sound-hole geometry of the violin's ancestors slowly evolved over centuries from simple circles to complex f-holes, the ratio of inefficient, acoustically inactive to total sound-hole area was decimated, roughly doubling air-resonance power efficiency. F-hole length then slowly increased by roughly 30% across two centuries in the renowned workshops of Amati, Stradivari and Guarneri, favouring instruments with higher air-resonance power, through a corresponding power increase of roughly 60%. By evolution-rate analysis, these changes are found to be consistent with mutations arising within the range of accidental replication fluctuations from craftsmanship limitations with subsequent selection favouring instruments with higher air-resonance power.

Surface gravity-wave lensing.

Here we show that a nonlinear resonance between oceanic surface waves caused by small seabed features (the so-called Bragg resonance) can be utilized to create the equivalent of lenses and curved mirrors for surface gravity waves. Such gravity wave lenses, which are merely small changes to the seafloor topography and therefore are surface noninvasive, can focus or defocus the energy of incident waves toward or away from any desired focal point. We further show that for a broadband incident wave spectrum (i.e., a wave group composed of a multitude of different-frequency waves), a polychromatic topography (occupying no more than the area required for a monochromatic lens) can achieve a broadband lensing effect. Gravity wave lenses can be utilized to create localized high-energy wave zones (e.g., for wave energy harvesting or creating artificial surf zones) as well as to disperse waves in order to create protected areas (e.g., harbors or areas near important offshore facilities). In reverse, lensing of oceanic waves may be caused by natural seabed features and may explain the frequent appearance of very high amplitude waves in certain bodies of water.

Versatile low-Reynolds-number swimmer with three-dimensional maneuverability.

We design and simulate the motion of a swimmer, the Quadroar, with three-dimensional translation and reorientation capabilities in low-Reynolds-number conditions. The Quadroar is composed of an I-shaped frame whose body link is a simple linear actuator and four disks that can rotate about the axes of flange links. The time symmetry is broken by a combination of disk rotations and the one-dimensional expansion or contraction of the body link. The Quadroar propels on forward and transverse straight lines and performs full three-dimensional reorientation maneuvers, which enable it to swim along arbitrary trajectories. We find continuous operation modes that propel the swimmer on planar and three-dimensional periodic and quasiperiodic orbits. Precessing quasiperiodic orbits consist of slow lingering phases with cardioid or multiloop turns followed by directional propulsive phases. Quasiperiodic orbits allow the swimmer to access large parts of its neighboring space without using complex control strategies. We also discuss the feasibility of fabricating a nanoscale Quadroar by photoactive molecular rotors.

Brownian motion of tethered nanowires.

Brownian motion of slender particles near a boundary is ubiquitous in biological systems and in nanomaterial assembly, but the complex hydrodynamic interaction in those systems is still poorly understood. Here, we report experimental and computational studies of the Brownian motion of silicon nanowires tethered on a substrate. An optical interference method enabled direct observation of microscopic rotations of the slender bodies in three dimensions with high angular and temporal resolutions. This quantitative observation revealed anisotropic and angle-dependent hydrodynamic wall effects: rotational diffusivity in inclined and azimuth directions follows different power laws as a function of the length, ∼ L(-2.5) and ∼ L(-3), respectively, and is more hindered for smaller inclined angles. In parallel, we developed an implicit simulation technique that takes the complex wire-wall hydrodynamic interactions into account efficiently, the result of which agreed well with the experimentally observed angle-dependent diffusion. The demonstrated techniques provide a platform for studying the microrheology of soft condensed matters, such as colloidal and biological systems near interfaces, and exploring the optimal self-assembly conditions of nanostructures.

Finite-depth capillary-gravity dromions.

It is known that the governing equations for the evolution of the envelope of weakly nonlinear capillary-gravity wave packets, the so-called Davey-Stewartson equation, admit dromion solutions in the limit of shallow water and strong surface tension, i.e., when kh≪1 and the Bond number (Bo) ≡T/ρgh^{2}>1/3 (where T is the surface tension coefficient and h the water depth). Here we show that capillary-gravity dromions exist beyond this limit for a broad range of finite water depths, i.e., for kh ≥ O(1), as well as for subcritical Bond numbers, i.e., for Bo < 1/3.