Slippery but Tough: The Rapid Fracture of Lubricated Frictional Interfaces.

We study the onset of friction for rough contacting blocks whose interface is coated with a thin lubrication layer. High speed measurements of the real contact area and stress fields near the interface reveal that propagating shear cracks mediate lubricated frictional motion. While lubricants reduce interface resistances, surprisingly they significantly increase the energy dissipated Γ during rupture. Moreover, lubricant viscosity affects the onset of friction but has no effect on Γ. Fracture mechanics provide a new way to view the otherwise hidden complex dynamics of the lubrication layer.

Failing softly: a fracture theory of highly-deformable materials.

Highly-deformable materials, from synthetic hydrogels to biological tissues, are becoming increasingly important from both fundamental and practical perspectives. Their mechanical behaviors, in particular the dynamics of crack propagation during failure, are not yet fully understood. Here we propose a theoretical framework for the dynamic fracture of highly-deformable materials, in which the effects of a dynamic crack are treated with respect to the nonlinearly deformed (pre-stressed/strained), non-cracked, state of the material. Within this framework, we derive analytical and semi-analytical solutions for the near-tip deformation fields and energy release rates of dynamic cracks propagating in incompressible neo-Hookean solids under biaxial and uniaxial loading. We show that moderately large pre-stressing has a marked effect on the stress fields surrounding a crack's tip. We verify these predictions by performing extensive experiments on the fracture of soft brittle elastomers over a range of loading levels and propagation velocities, showing that the newly developed framework offers significantly better approximations to the measurements than standard approaches at moderately large levels of external loadings and high propagation velocities. This framework should be relevant to the failure analysis of soft and tough, yet brittle, materials.

Necessary conditions for mode interactions in parametrically excited waves.

We study the spatial and temporal structure of nonlinear states formed by parametrically excited waves on a fluid surface (Faraday instability), in a highly dissipative regime. Short-time dynamics reveal that 3-wave interactions between different spatial modes are only observed when the modes' peak values occur simultaneously. The temporal structure of each mode is functionally described by the Hill's equation and is unaffected by which nonlinear interaction is dominant.

Dynamics of precursors to frictional sliding.

We measure the spatial and temporal behavior of the true contact area A along a rough spatially extended interface between two blocks in frictional contact. Upon the application of shear the onset of motion is preceded by a discrete sequence of cracklike precursors, which are initiated at shear levels that are well below the threshold for static friction. These precursors arrest well before traversing the entire interface. They systematically increase in length with the applied shear force and significantly redistribute the true contact area along the interface. Thus, when frictional sliding occurs, the initially uniform contact area along the interface has already evolved to one that is highly nonuniform in space.

Contact area measurements reveal loading-history dependence of static friction.

We perform quantitative measurements of the actual area of contact, A, formed by two rough solids that are subjected to different normal loading protocols. We show that microscopic motion, induced by Poisson contraction or expansion, produces a strong memory dependence of on the loading history with a large corresponding influence on the system's frictional strength. These effects, together with accompanying transient dynamics, are independent of humidity, loading rates, and material contrast across the interface.

Grid states and nonlinear selection in parametrically excited surface waves.

Interacting surface waves, parametrically excited by two commensurate frequencies (Faraday waves), yield a rich family of nonlinear states, which result from a variety of three-wave resonant interactions. By perturbing the system with a third frequency, we selectively favor different nonlinear wave interactions. Where quadratic nonlinearities are dominant, the only observed patterns correspond to "grid" states. Grid states are superlattices in which two corotated sets of critical wave vectors are spanned by a sublattice whose basis states are linearly stable modes. Specific driving phase combinations govern the selection of different grid states.

Universality and hysteretic dynamics in rapid fracture.

Experiments in the dynamic fracture of brittle polyacrylamide gels show that a single-crack state undergoes a hysteretic transition to the microbranching instability with a characteristic activation time. Quantitative measurements also indicate that features such as crack front inertia, self-focusing of microbranches, and the appearance of front waves are universal attributes of dynamic fracture.

Control of spatiotemporal disorder in parametrically excited surface waves.

Interacting surface waves, parametrically excited by two commensurate frequencies, yield a number of nonlinear states. Near the system's bicritical point, a state, highly disordered in space and time, results from competition between nonlinear states. Experimentally, this disordered state can be rapidly stabilized to a variety of nonlinear states via open-loop control with a small-amplitude third frequency excitation, whose temporal symmetry governs the temporal and the spatial symmetry of the selected nonlinear state. This technique also excites rapid switching between nonlinear states.

Pattern formation in two-frequency forced parametric waves.

We present an experimental investigation of superlattice patterns generated on the surface of a fluid via parametric forcing with two commensurate frequencies. The spatiotemporal behavior of four qualitatively different types of superlattice patterns is described in detail. These states are generated via a number of different three-wave resonant interactions. They occur either as symmetry-breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two primary unstable modes generated by the two forcing frequencies. A coherent picture of these states together with the phase space in which they appear is presented. In addition, we describe a number of new superlattice states generated by four-wave interactions that arise when symmetry constraints rule out three-wave resonances.

Crack front waves and the dynamics of a rapidly moving crack.

Crack front waves are nonlinear localized waves that propagate along the leading edge of a crack. They are generated by both the interaction of a crack with a localized material inhomogeneity and the intrinsic formation of microbranches. Front waves are shown to transport energy, generate surface structure, and lead to localized velocity fluctuations. Their existence locally imparts inertia, which is not incorporated in current theories of fracture, to initially "massless" cracks. This, coupled to microbranch formation, yields both inhomogeneity and scaling behavior within the fracture surface structure.

Shock wave criterion for propagating solitary states in driven surface waves.

Highly localized solitary states are observed to propagate along the surface of a thin two-dimensional fluid layer. The states are driven by means of a spatially uniform, temporally periodic, vertical acceleration (Faraday experiment) in a highly dissipative fluid. These states are shown to be formed by coupled fronts that propagate, periodically, as shock waves. A criterion for their formation based on shock initiation is presented. Both the characteristic form and interaction dynamics of the solitary states can be understood in this picture.

Propagating solitary waves along a rapidly moving crack front.

A rapidly moving crack in a brittle material is often idealized as a one-dimensional object with a singular tip, moving through a two-dimensional material. However, in real three-dimensional materials, tensile cracks form a planar surface whose edge is a rapidly moving one-dimensional singular front. The dynamics of these fronts under repetitive interaction with material inhomogeneities (asperities) and the morphology of the fracture surface that they create are not yet understood. Here we show that perturbations to a crack front in a brittle material result in long-lived and highly localized waves, which we call 'front waves' These waves exhibit a unique characteristic shape and propagate along the crack front at approximately the Rayleigh wave speed (the speed of sound along a free surface). Following interaction, counter-propagating front waves retain both their shape and amplitude. They create characteristic traces along the fracture surface, providing cracks with both inertia and a new mode of dissipation. Front waves are intrinsically three-dimensional, and cannot exist in conventional two-dimensional theories of fracture. Because front waves can transport and distribute asperity-induced energy fluctuations throughout the crack front, they may help to explain how cracks remain a single coherent entity, despite repeated interactions with randomly dispersed asperities.

Two-mode rhomboidal states in driven surface waves

Two-mode rhomboid patterns are generated experimentally via two-frequency parametric forcing of surface waves. These patterns are formed by the simple nonlinear resonance: k-->'2-k-->(2) = k-->(1) where k(1) and k(2)( = k(')(2)) are concurrently excited eigenmodes. The state possesses a direction-dependent time dependence described by a superposition of the two modes, and a dimensionless scaling delineating the state's region of existence is presented. We also show that 2n-fold quasipatterns naturally arise from these states when the coupling angle between k-->(2) and k-->'2 is 2pi/n.

Temporally harmonic oscillons in newtonian fluids

Stationary, highly localized (oscillon) structures are observed in a Newtonian fluid when nonlinear surface waves are parametrically excited with two frequencies. Oscillons have a characteristic structure, that of periodically self-focusing jets. In contrast to previously observed oscillons in highly non-Newtonian media, these states are temporally harmonic with the forcing. For wave amplitudes greater than a critical value, they nucleate from an initial pattern via a hysteretic bifurcation, and can therefore be localized on a background of patterns with a variety of different spatial symmetries.

Turbulence and wave breaking effects on air-water gas exchange

We present an experimental characterization of the effects of turbulence and breaking gravity waves on air-water gas exchange in standing waves. We identify two regimes that govern aeration rates: turbulent transport when no wave breaking occurs and bubble dominated transport when wave breaking occurs. In both regimes, we correlate the qualitative changes in the aeration rate with corresponding changes in the wave dynamics. In the latter regime, the strongly enhanced aeration rate is correlated with measured acoustic emissions, indicating that bubble creation and dynamics dominate air-water exchange.

Perception of musical tension for nontonal orchestral timbres and its relation to psychoacoustic roughness.

Can tension in nontonal music be expressed without dynamic or rhythmic cues? Perceptual theories of tonal harmony predict that psychoacoustic roughness plays an important role in the perception of this tension. We chose a set of orchestrated chords from a nontonal piece and investigated listeners' judgments of musical tension and roughness. Paired comparisons yielded psychophysical scales of tension and roughness. Two experiments established distinct levels of these two attributes across chords. A model simulation reproduced the experimental roughness measures. The results indicate that nontonal tension could be perceived consistently on the basis of timbral differences and that it was correlated with roughness, the correlation being stronger as the perceptual salience of other attributes (such as high-pitched tones or tonal intervals) was reduced.

Singularity dynamics in curvature collapse and jet eruption on a fluid surface

Finite-time singularities--local divergences in the amplitude or gradient of a physical observable at a particular time--occur in a diverse range of physical systems. Examples include singularities capable of damaging optical fibres and lasers in nonlinear optical systems, and gravitational singularities associated with black holes. In fluid systems, the formation of finite-time singularities cause spray and air-bubble entrainment, processes which influence air-sea interaction on a global scale. Singularities driven by surface tension have been studied in the break-up of pendant drops and liquid sheets. Here we report a theoretical and experimental study of the generation of a singularity by inertial focusing, in which no break-up of the fluid surface occurs. Inertial forces cause a collapse of the surface that leads to jet formation; our analysis, which includes surface tension effects, predicts that the surface profiles should be describable by a single universal exponent. These theoretical predictions correlate closely with our experimental measurements of a collapsing surface singularity. The solution can be generalized to apply to a broad class of singular phenomena.

Covalent attachment of DNA oligonucleotides to glass.

A method for synthesizing DNA directly on glass is presented. The process is based on pretreatment of glass with boiling hydrochloric acid, thus exposing the hydroxyl groups of the glass. Phosphite-triester chemistry was used to directly attach the first nucleotide to a glass plate via a covalent bond between the hydroxyl group of the glass and the phosphate group of the protected deoxyribonucleotide. Standard molecular biology procedures, such as ligation and restriction digest, were efficiently performed on the glass synthesized oligonucleotide, with the added benefit of extreme ease of handling.