Open-system force-elongation relationship of collagen in chemo-mechanical equilibrium with water.

A significant deformation mechanism of collagen at low loads is molecular uncoiling and rearrangement. Although the effect of hydration and cross-linking has been investigated at larger loads when collagen undergoes molecular sliding, their effects on collagen molecular reorganization remain unclear. Here we develop two thermodynamic models that use the notion of open-system elasticity to elucidate the effect of swelling due to water uptake during deformation of collagen networks under low and high cross-linking conditions. With low crosslinking, entropic contributions dominate resulting in rejection of solvent from the polymer network leading to reduced collagen stiffness with increased loads. Contrarily, high cross-linking inhibits initial coiling and structural kinking and the mechanical behavior is dominated by elastic energy. In this configuration, the solvent content depends on the sign of the applied load resulting in a non-linear open-system stress-strain relationship. The models provide insight on the parameters that impact the stress-strain relationships of hydrated collagen and can inform the way collagenous matrices are treated both in medical and laboratory settings.

Realizing acoustic qubit analogues with nonlinearly tunable phi-bits in externally driven coupled acoustic waveguides.

Using experiments and theory, we investigate the behavior of nonlinear acoustic modes in a physical system composed of an array of three coupled acoustic waveguides, two of which are externally driven with two different frequencies. Nonlinear modes with frequency given by linear combinations of the driving frequencies are realizations of so-called logical phi-bits. A phi-bit is a two-state degree of freedom of an acoustic wave, which can be in a coherent superposition of states with complex amplitude coefficients, i.e., a qubit analogue. We demonstrate experimentally that phi-bit modes are supported in the array of waveguides. Using perturbation theory, we show that phi-bits may result from the intrinsic nonlinearity of the material used to couple the waveguides. We have also isolated possible effects on phi-bit states associated with the systems' electronics, transducers and ultrasonic coupling agents used to probe the array and that may introduce extrinsic nonlinearities. These extrinsic effects are shown to be easily separable from the intrinsic behavior. The intrinsic behavior includes sharp jumps in phi-bit phases occurring over very narrow ranges of driving frequency. These jumps may also exhibit hysteretic behavior dependent on the direction of driving frequency tuning. The intrinsic states of phi-bits and multiple nonlinearly correlated phi-bits may serve as foundation for robust and practical quantum-analogue information technologies.

Exponentially Complex "Classically Entangled" States in Arrays of One-Dimensional Nonlinear Elastic Waveguides.

We demonstrate theoretically, using multiple-time-scale perturbation theory, the existence of nonseparable superpositions of elastic waves in an externally driven elastic system composed of three one-dimensional elastic wave guides coupled via nonlinear forces. The nonseparable states span a Hilbert space with exponential complexity. The amplitudes appearing in the nonseparable superposition of elastic states are complex quantities dependent on the frequency of the external driver. By tuning these complex amplitudes, we can navigate the state's Hilbert space. This nonlinear elastic system is analogous to a two-partite two-level quantum system.

Evidence for hidden order in a nonlinear model elastic system.

Hidden order may arise in strongly correlated systems even if there is an apparent lack of long-range order as measured by local order parameters. This phenomenon has been essentially associated with topological order in quantum systems. Here, we demonstrate the emergence of hidden order in a 1D non-linear classical mechanical system that supports rotational degrees of freedom. The potential energy of the model system creates a bistable system for which hidden order emerges with the introduction of a biquadratic term. To our surprise, we discover that varying the strength of the biquadratic term leads to four distinct phases quantified by the behaviors of the Néel and string order parameters. Three of these phases are locally disordered. Hidden order is identified by a string order parameter that shows correlations with significantly longer range than the Néel order parameter. The hidden order correlation length diverges as the kinetic energy of the system is lowered with a critical exponent ~0.5. The observation of hidden order in a mechanical system reveals that instability and non-linearity may play critical roles in the generation of nonlocal long-range correlations in apparently locally disordered systems.

Giant frequency down-conversion of the dancing acoustic bubble.

We have demonstrated experimentally the existence of a giant frequency down-conversion of the translational oscillatory motion of individual submillimeter acoustic bubbles in water in the presence of a high frequency (500 kHz) ultrasonic standing wave. The frequency of the translational oscillations (~170 Hz) is more than three orders of magnitude smaller than that of the driving acoustic wave. We elucidate the mechanism of this very slow oscillation with an analytical model leading to an equation of translational motion of a bubble taking the form of Mathieu's equation. This equation illuminates the origin of the giant down conversion in frequency as arising from an unstable equilibrium. We also show that bubbles that form chains along the direction of the acoustic standing wave due to radiation interaction forces exhibit also translation oscillations that form a spectral band. This band extends approximately from 130 Hz up to nearly 370 Hz, a frequency range that is still at least three orders of magnitude lower than the frequency of the driving acoustic wave.

Effect of sound on gap-junction-based intercellular signaling: Calcium waves under acoustic irradiation.

We present a previously unrecognized effect of sound waves on gap-junction-based intercellular signaling such as in biological tissues composed of endothelial cells. We suggest that sound irradiation may, through temporal and spatial modulation of cell-to-cell conductance, create intercellular calcium waves with unidirectional signal propagation associated with nonconventional topologies. Nonreciprocity in calcium wave propagation induced by sound wave irradiation is demonstrated in the case of a linear and a nonlinear reaction-diffusion model. This demonstration should be applicable to other types of gap-junction-based intercellular signals, and it is thought that it should be of help in interpreting a broad range of biological phenomena associated with the beneficial therapeutic effects of sound irradiation and possibly the harmful effects of sound waves on health.

A first-principles characterization of water adsorption on forsterite grains.

Numerical simulations examining chemical interactions of water molecules with forsterite grains have demonstrated the efficacy of nebular gas adsorption as a viable mechanism for water delivery to the terrestrial planets. Nevertheless, a comprehensive picture detailing the water-adsorption mechanisms on forsterite is not yet available. Towards this end, using accurate first-principles density functional theory, we examine the adsorption mechanisms of water on the (001), (100), (010) and (110) surfaces of forsterite. While dissociative adsorption is found to be the most energetically favourable process, two stable associative adsorption configurations are also identified. In dual-site adsorption, the water molecule interacts strongly with surface magnesium and oxygen atoms, whereas single-site adsorption occurs only through the interaction with a surface Mg atom. This results in dual-site adsorption being more stable than single-site adsorption.

Phase-controlling phononic crystals: realization of acoustic Boolean logic gates.

A phononic crystal (PC) consisting of a square array of cylindrical polyvinylchloride inclusions in air is used to construct a variety of acoustic logic gates. In a certain range of operating frequencies, the PC band structure shows square-like equi-frequency contours centered off the gamma point. This attribute allows for the realization of non-collinear wave and group velocity vectors in the PC wave vector space. This feature can be utilized to control with great precision, the relative phase between propagating acoustic waves in the PC. By altering the incidence angle of the impinging acoustic beams or varying the PC thickness, interferences occur between acoustic wave pairs. It is recognized that information can be encoded with this mechanism (e.g., wave amplitudes/interference patterns) and accordingly to construct a series of logic gates emulating Boolean functions. The NAND, XOR, and NOT gates are demonstrated with finite-difference time-domain simulations of acoustic waves impinging upon the PC.

Modeling the coupling of reaction kinetics and hydrodynamics in a collapsing cavity.

We introduce a model of cavitation based on the multiphase Lattice Boltzmann method (LBM) that allows for coupling between the hydrodynamics of a collapsing cavity and supported solute chemical species. We demonstrate that this model can also be coupled to deterministic or stochastic chemical reactions. In a two-species model of chemical reactions (with a major and a minor species), the major difference observed between the deterministic and stochastic reactions takes the form of random fluctuations in concentration of the minor species. We demonstrate that advection associated with the hydrodynamics of a collapsing cavity leads to highly inhomogeneous concentration of solutes. In turn these inhomogeneities in concentration may lead to significant increase in concentration-dependent reaction rates and can result in a local enhancement in the production of minor species.

Experimental and theoretical evidence for subwavelength imaging in phononic crystals.

We show experimentally and theoretically that super resolution can be achieved while imaging with a flat lens consisting of a phononic crystal exhibiting negative refraction. This phenomenon is related to the coupling between the incident evanescent waves and a bound slab mode of the phononic crystal lens, leading to amplification of evanescent waves by the slab mode. Super resolution is only observed when the source is located very near to the lens, and is very sensitive to the location of the source parallel to the lens surface as well as to site disorder in the phononic crystal lattice.

Formation of copper nanowires by electroless deposition using microtubules as templates.

Microtubules (MTs) are self-assembling, protein-based, tubular structures several micrometers long with outer and inner diameters of 25 nm and 15 nm, respectively. This aspect ratio makes MTs ideal templates for producing nanowires for applications such as electrical nano-interconnects. MTs are poorly conductive and their use as interconnects necessitates their metallization. We report a process for metallization of MTs with copper using a biologically benign electroless deposition chemistry consisting of copper sulfate solution containing acetic acid as a complexant and ascorbic acid as reducing agent. The pH of the plating bath is controlled such that copper metallization occurs without disassembling the MTs. Electron microscopic characterization of the morphology and dimensions of the copper nanowires shows that metallization for approximately 1 minute produces a uniform nanowire with an average diameter of approximately 15 nm, suggesting that metallization is initiated selectively from the MT inner core.

Dynamic compound wavelet matrix method for multiphysics and multiscale problems.

The paper presents the dynamic compound wavelet method (dCWM) for modeling the time evolution of multiscale and/or multiphysics systems via an "active" coupling of different simulation methods applied at their characteristic spatial and temporal scales. Key to this "predictive" approach is the dynamic updating of information from the different methods in order to adaptively and accurately capture the temporal behavior of the modeled system with higher efficiency than the (nondynamic) "corrective" compound wavelet matrix method (CWM), upon which the proposed method is based. The system is simulated by a sequence of temporal increments where the CWM solution on each increment is used as the initial conditions for the next. The numerous advantages of the dCWM method such as increased accuracy and computational efficiency in addition to a less-constrained and a significantly better exploration of phase space are demonstrated through an application to a multiscale and multiphysics reaction-diffusion process in a one-dimensional system modeled using stochastic and deterministic methods addressing microscopic and macroscopic scales, respectively.

Effect of tubulin diffusion on polymerization of microtubules.

The dynamics of microtubules (MT's) growing from a nucleation center is simulated with a kinetic Monte Carlo model that includes tubulin diffusion. In the limit of fast diffusion (homogeneous tubulin concentration), MT growth is synchronous and bounded. The microtubules form an aster with a monotonously decreasing long-time distribution of lengths. Slow tubulin diffusion leads to rapid dephasing in the growth dynamics, unbounded growth of some MT's, spatial inhomogeneities, and morphological change toward a morphology with bounded short MT's located in the nucleation center and unbounded long MT's with narrowly distributed lengths. The transition from unbounded to bounded growth is driven by the competition between the reaction rate of the tubulin assembly and the tubulin's diffusion rate. While the present study reports the effect of the tubulin diffusion coefficient on the transition, the results of the simulations are qualitatively comparable to the morphological and dynamical changes of centrosome-nucleated MT's from interphase to mitosis in cellular systems where the transition is regulated by the reaction rates.

Adsorption of a microtubule on a charged surface affects its disassembly dynamics.

The dynamics of disassembly of microtubules deposited on surfaces is shown to be strongly dependent on the electrostatic interaction between the microtubule and the substrate. Fluorescence microscopy of microtubules adsorbed on a Poly-L-Lysine film and immersed in pure water show a drastic decrease in disassembly velocity compared to the microtubules in bulk water solutions. While microtubules suspended in pure water disassemble in seconds, the dissociation velocity of microtubules adsorbed on a Poly-L-Lysine film ranges from 0.8 to 1.0 microm/min in pure water. Kinetic Monte Carlo simulations of the microtubule dynamics indicate that a decrease in the dissociation velocity of unstable microtubules can be achieved by reducing the heterodimer dissociation rate constant of tubulin heterodimers constituting a single protofilament, adsorbed to the Poly-L-Lysine film. This model suggests that the reduction of the dissociation velocity originates from the electrostatic interactions between the positively charged amino groups of the Poly-L-Lysine film and the negatively charged microtubule surface.

Tunable filtering and demultiplexing in phononic crystals with hollow cylinders.

Acoustic band gap (ABG) materials constituted of steel hollow cylinders immersed in water can exhibit a tunable narrow pass band (NPB) located inside their gap. We theoretically investigate, using the finite difference time domain (FDTD) method, the properties of waveguides composed of a row of hollow cylinders in a two-dimensional (2D) phononic crystal made of filled steel cylinders. These waveguides exhibit NPB's at frequencies slightly higher than their infinite periodic ABG counterpart. The frequency of the waveguide's NPB can be selected by adjusting the inner radius of the hollow cylinders or by changing the nature of the fluid that fills them. We show that a waveguide constituted of a row of hollow cylinders with different inner radii can transport waves at two different frequencies. By selectively filling the cylinders with water or mercury we have created an active device that permits the transmission of waves at one, both, or neither of these frequencies. Finally, we examine the multiplexing and demultiplexing capabilities of Y shaped waveguides constituted of hollow cylinders.

Phononic crystal with low filling fraction and absolute acoustic band gap in the audible frequency range: a theoretical and experimental study.

The propagation of acoustic waves in a two-dimensional composite medium constituted of a square array of parallel copper cylinders in air is investigated both theoretically and experimentally. The band structure is calculated with the plane wave expansion (PWE) method by imposing the condition of elastic rigidity to the solid inclusions. The PWE results are then compared to the transmission coefficients computed with the finite difference time domain (FDTD) method for finite thickness composite samples. In the low frequency regime, the band structure calculations agree with the FDTD results indicating that the assumption of infinitely rigid inclusion retains the validity of the PWE results to this frequency domain. These calculations predict that this composite material possesses a large absolute forbidden band in the domain of the audible frequencies. The FDTD spectra reveal also that hollow and filled cylinders produce very similar sound transmission suggesting the possibility of realizing light, effective sonic insulators. Experimental measurements show that the transmission through an array of hollow Cu cylinders drops to noise level throughout frequency interval in good agreement with the calculated forbidden band.

Theory of acoustic scattering by supported ridges at a solid-liquid interface.

We combine a general Green's function formalism and an approach due to Nyborg [W. L. Nyborg, in Acoustic Streaming, Physical Acoustics, edited by W. P. Mason (Academic, London, 1965), Vol. II B, Chap. 11] to calculate the first-order pressure and second-order pressure gradient fields in the vicinity of solid inhomogeneities at a solid/liquid interface. We treat the problem of scattering of an incident acoustic plane wave by a single ridge and two parallel ridges separated by a trench on a planar substrate. The calculated vibrational density of states shows the existence of resonances at low frequencies, especially in the case of a trench. Excitation of a trench resonant vibrational mode enhances the magnitude of the first-order pressure and of the second-order pressure gradient. The resonant frequencies of a trench decrease and the pressure enhancement increases with increasing aspect ratio of the ridges (height to width).

Experimental and theoretical evidence for the existence of absolute acoustic band gaps in two-dimensional solid phononic crystals.

Experimental measurements of acoustic transmission through a solid-solid two-dimensional binary-composite medium constituted of a triangular array of parallel circular steel cylinders in an epoxy matrix are reported. Attention is restricted to propagation of elastic waves perpendicular to the cylinders. Measured transmitted spectra demonstrate the existence of absolute stop bands, i.e., band gaps independent of the direction of propagation in the plane perpendicular to the cylinders. Theoretical calculations of the band structure and transmission spectra using the plane wave expansion and the finite difference time domain methods support unambiguously the absolute nature of the observed band gaps.