The saline oscillator consists of an inner vessel containing salt water partially immersed in an outer vessel of fresh water, with a small orifice in the center of the bottom of the inner vessel. There is a cyclic alternation between salt water flowing downwards out of the inner vessel into the outer vessel through the orifice and fresh water flowing upwards into the inner vessel from the outer vessel through that same orifice. We develop a very stable (i.e., stationary) version of this saline oscillator. We first investigate the response of the oscillator to periodic forcing with a train of stimuli $(\text{period}=T_{\mathrm{p}})$ of large amplitude. Each stimulus is the quick injection of a fixed volume of fresh water into the outer vessel followed immediately by withdrawal of that very same volume. For $T_{\mathrm{p}}$ sufficiently close to the intrinsic period of the oscillator $\left(T_0\right)$, there is 1:1 synchronization or phase locking between the stimulus train and the oscillator. As $T_{\mathrm{p}}$ is decreased below $T_0$, one finds the succession of phase-locking rhythms: 1:1, 2:2, 2:1, 2:2, and 1:1. As $T_{\mathrm{p}}$ is increased beyond $T_0$, one encounters successively 1:1, 1:2, 2:4, 2:3, 2:4, and 1:2 phase-locking rhythms. We next investigate the phase-resetting response, in which injection of a single stimulus transiently changes the period of the oscillation. By systematically changing the phase of the cycle at which the stimulus is delivered (the old phase), we construct the new-phase—old-phase curve (the phase transition curve), from which we then develop a one-dimensional finite-difference equation (“map”) that predicts the response to periodic stimulation. These predicted phase-locking rhythms are close to the experimental findings. In addition, iteration of the map predicts the existence of bistability between two different 1:1 rhythms, which was then searched for and found experimentally. Bistability between 1:1 and 2:2 rhythms is also encountered. Finally, with one exception, numerical modeling with a phenomenologically derived Rayleigh oscillator reproduces all of the experimental behavior.

An experimental study of droplet breakup in T-shaped microfluidic junctions is presented in which the capillary number and flow rate ratio are varied over a wide range for several different viscosity ratios and several different ratios of the inlet channel widths. The range of conditions corresponds to the region in which both the squeezing pressure that arises when the emerging interface obstructs the channel and the viscous shear stress on the emerging interface strongly influence the process. In this regime, the droplet volume depends on the capillary number, the flow rate ratio, and the ratio of inlet channel widths, which controls the degree of confinement of the droplets. The viscosity ratio influences the droplet volume only when the viscosities are similar. When there is a large viscosity contrast in which the dispersed-phase liquid is at least 50 times smaller than the continuous-phase liquid, the resulting size is independent of the viscosity ratio and no transition to a purely squeezing regime appears. In this case, both the droplet volume and the droplet production frequency obey power-law behavior with the capillary number, consistent with expectations based on mass conservation of the dispersed-phase liquid. Finally, scaling arguments are presented that result in predicted droplet volumes that depend on the capillary number, flow rate ratio, and width ratio in a qualitatively similar way to that observed in experiments.

The extraction of the Green’s function by cross correlation of waves recorded at two receivers nowadays finds much application. We show that for an arbitrary small scatterer, the cross terms of scattered waves give an unphysical wave with an arrival time that is independent of the source position. This constitutes an apparent inconsistency because theory predicts that such spurious arrivals do not arise, after integration over a complete source aperture. This puzzling inconsistency can be resolved for an arbitrary scatterer by integrating the contribution of all sources in the stationary phase approximation to show that the stationary phase contributions to the source integral cancel the spurious arrival by virtue of the generalized optical theorem. This work constitutes an alternative derivation of this theorem. When the source aperture is incomplete, the spurious arrival is not canceled and could be misinterpreted to be part of the Green’s function. We give an example of how spurious arrivals provide information about the medium complementary to that given by the direct and scattered waves; the spurious waves can thus potentially be used to better constrain the medium.

The long-time behavior of the first two moments and the correlation function for the output signal of a harmonic oscillator with fluctuating frequency subjected to an external periodic force and an additive thermal noise is considered analytically. The colored fluctuations of the oscillator frequency are modeled as a three-level Markovian noise. Using the Shapiro-Loginov formula, the exact expressions of several stochastic resonance (SR) characteristics such as the spectral amplification, the variance of the output signal, the signal-to-noise ratio, and the SR gain have been calculated. The nonmonotonic dependence of the SR characteristics versus the noise parameters as well as versus the input signal frequency and also the conditions for the appearance of energetic instability are analyzed. In particular, the multiresonancelike behavior of the variance and the signal-to-noise ratio as functions of the noise correlation time are observed and the connection between the occurrence of energetic instability and the phenomenon of stochastic multiresonance is established. Some unexpected effects such as the hypersensitive response of the spectral amplification to small variations of the noise amplitude encountered in the case of a large flatness of the colored noise are also discussed.

We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular media and wet foams. We assume that the intensity reflectance of disks is a constant $r$. We present an analytic expression for the transport mean free path $l^{*}$ in terms of the velocity of light in the disks and host medium, radius $R$ and packing fraction of the disks, and the intensity reflectance. For glass beads immersed in air or water, we estimate transport mean free paths about half the experimental ones. For air bubbles immersed in water, $l^{*}∕R$ is a linear function of $1∕\epsilon$, where $\epsilon$ is the liquid volume fraction of the model wet foam. This throws light on the empirical law of Vera et al. [Appl. Opt. 40, 4210 (2001)] and promotes more realistic models.

Probability distributions which can be obtained from superpositions of Gaussian distributions of different variances $v={\sigma }^2$ play a favored role in quantum theory and financial markets. Such superpositions need not necessarily obey the Chapman-Kolmogorov semigroup relation for Markovian processes because they may introduce memory effects. We derive the general form of the smearing distributions in $v$ which do not destroy the semigroup property. The smearing technique has two immediate applications. It permits simplifying the system of Kramers-Moyal equations for smeared and unsmeared conditional probabilities, and can be conveniently implemented in the path integral calculus. In many cases, the superposition of path integrals can be evaluated much easier than the initial path integral. Three simple examples are presented, and it is shown how the technique is extended to quantum mechanics.

Axial banding in rotating tumblers has been experimentally observed, but the dependence of band formation on the relative concentration of the bidisperse particles has not been thoroughly examined. We consider axial band formation and coarsening for dry and liquid granular systems of bidisperse mixtures of glass beads where the small particle volume fraction ranges from 10% to 90% in half-filled tumblers for several rotation rates. Single bands form for small particle volume fractions as low as 10% and as high as 90%, usually near the end walls. Band formation along the entire length of the tumbler is less likely at very low or very high volume fractions. After many rotations the segregation pattern coarsens, and for small particle volume fractions of 50% and greater, the coarsening is logarithmic. For very low or very high small particle volume fractions, the rate of coarsening is either not logarithmic or coarsening does not occur within the duration of the experiment (600 rotations). When bands form, the width of the band for either the small or large particles scales with the tumbler diameter.

The ordered configurations of a monolayer of interacting magnetic dipoles confined in a circular parabolic potential are investigated as a function of the dipole moment of the particles. Despite the circular confinement, we find very asymmetric ordered structures like chains and Y-shaped configurations when a magnetic field is applied parallel to the plane of the particles. The normal-mode spectrum of the particles and its dependence on the magnetic field and the strength of the dipole moment of the particles are studied. The vibrational and rotational modes of the spectrum, which are associated with the stability of the system, are investigated in detail. The number of particles is varied and we found different ordering of the particles for different values of the dipole moment and the magnetic field. A ring structure with a large number of particles is observed for high values of the dipole moment of the particles.

We measure hydrodynamic interactions between colloidal particles confined in a thin sheet of fluid. The reduced dimensionality, compared to a bulk fluid, increases dramatically the range of couplings. Using optical tweezers we force a two body system along the eigenmodes of the mobility tensor and find that eigenmobilities change logarithmically with particle separation. At a hundred radii distance, the mobilities for rigid and relative motions differ by a factor of 2, whereas in bulk fluids, they would be practically indistinguishable. A two dimensional counterpart of Oseen hydrodynamic tensor quantitatively reproduces the observed behavior, once the relevant boundary conditions are recognized. These results highlight the importance of dimensionality for transport and interactions in colloidal systems and proteins in biological membranes.

Coacervation is a dense liquid-liquid phase separation and herein we report coacervation of protein bovine serum albumin (BSA) in the presence of polyelectrolyte sodium polystyrene sulfonate (NaPSS) under varying solution conditions. Small-angle neutron scattering (SANS) measurements have been performed on above protein-polyelectrolyte complexes to study the structural evolution of the process that leads to coacervation and the phase separated coacervate as a function of solution $p\mathrm{H}$, protein-polyelectrolyte ratio and ionic strength. SANS study prior to phase separation on the BSA-NaPSS complex shows a fractal structure representing a necklace model of protein macromolecules randomly distributed along the polystyrene sulfonate chain. The fractal dimension of the complex decreases as $p\mathrm{H}$ is shifted away from the isoelectric point $(\sim 4.7)$ of BSA protein, which indicates the decrease in the compactness of the complex structure due to increase in the charge repulsion between the protein macromolecules bound to the polyelectrolyte. Concentration-dependence studies of the polyelectrolyte in the complex suggest coexistence of two populations of polyelectrolytes, first one fully saturated with proteins and another one free from proteins. Coacervation phase has been obtained through the turbidity measurement by varying $p\mathrm{H}$ of the aqueous solution containing protein and polyelectrolyte from neutral to acidic regime to get them to where the two components are oppositely charged. The spontaneous formation of coacervates is observed for $p\mathrm{H}$ values less than 4. SANS study on coacervates shows two length scales related to complex aggregations (mesh size and overall extent of the complex) hierarchically branched to form a larger network. The mesh size represents the distance between cross-linked points in the primary complex, which decreases with increase in ionic strength and remains the same on varying the protein-polyelectrolyte ratio. On the other hand, the overall extent of the complex shows a similar structure irrespective of varying ionic strength and protein-polyelectrolyte ratio. A large fraction $(\sim 50\%)$ of protein-polyelectrolyte complexes is also found to be free in the supernatant after the coacervation.

We report an experimental and theoretical study of the radial elasticity of tobacco mosaic virus (TMV) nanotubes. An atomic force microscope tip is used to apply small radial indentations to deform TMV nanotubes. The initial elastic response of TMV nanotubes can be described by finite-element analysis in $5\mathrm{nm}$ indentation depths and Hertz theory in $1.5\mathrm{nm}$ indentation depths. The derived radial Young’s modulus of TMV nanotubes is $0.92\pm 0.15\mathrm{GPa}$ from finite-element analysis and $1.0\pm 0.2\mathrm{GPa}$ from the Hertz model, which are comparable with the reported axial Young’s modulus of $1.1\mathrm{GPa}$ [Falvo et al., Biophys. J. 72, 1396 (1997)].

Microscale optical breakdown induced in bulk pure water by high-power nanosecond KrF laser pulses was studied using optical transmission and contact broadband photoacoustic techniques. The breakdown has been identified as a sharp transmission drop coinciding with the appearance of unipolar compressive acoustic pulses, both indicating a thresholdlike rise of local intrinsic absorption in the micrometer-scale laser focal volume. The acoustic pulses, which are much broader than the exciting laser pulse and show a strongly reduced far-field diffraction effect, result from breakdown-induced millimeter-sized steam bubbles. The acoustic pulse amplitudes exhibit a sub-linear $(\propto I^{3∕4})$ pressure dependence on the laser intensity $I$ characteristic of subcritical electron-ion plasma and demonstrating the avalanche enhancement of two-photon ionization above the breakdown threshold until the appearance of the critical plasma. In the critical plasma regime, where the transmission and the acoustic signals slowly vary as a function of laser intensity, the main acoustic pulse is preceded by nanosecond and sub-$\mu \mathrm{s}$ prepulses, where the first one represents a GPa-level plasma-driven shock wave and the second one adjacent to the main pulse appears due to weak submillimeter-long heating of water surrounding the hot plasma by its bremsstrahlung radiation, indicating significant dissociation of water molecules in the plasma.

Using conventional methods, a laser pulse can be focused down to around $6–8\mu \mathrm{m}$, but further reduction of the spot size has proven to be difficult. Here it is shown by particle-in-cell simulation that with a hollow cone an intense laser pulse can be reduced to a tiny, highly localized, spot of around $1\mu \mathrm{m}$ radius, accompanied by much enhanced light intensity. The pulse shaping and focusing effect is due to a nonlinear laser-plasma interaction on the inner surface of the cone. When a thin foil is attached to the tip of the cone, the cone-focused light pulse compresses and accelerates the ions in its path and can punch through the thin target, creating highly localized energetic ion bunches of high density.

The behavior of large-scale vortices governed by the discrete nonlinear Schrödinger equation is studied. Using a discrete version of modulation theory, it is shown how vortices are trapped and stabilized by the self-consistent Peierls-Nabarro potential that they generate in the lattice. Large-scale circular and polygonal vortices are studied away from the anticontinuum limit, which is the limit considered in previous studies. In addition numerical studies are performed on large-scale, straight structures, and it is found that they are stabilized by a nonconstant mean level produced by standing waves generated at the ends of the structure. Finally, numerical evidence is produced for long-lived, localized, quasiperiodic structures.

We study localized modes on the surface of a three-dimensional dynamical lattice. The stability of these structures on the surface is investigated and compared to that in the bulk of the lattice. Typically, the surface makes the stability region larger, an extreme example of that being the three-site “horseshoe”-shaped structure, which is always unstable in the bulk, while at the surface it is stable near the anticontinuum limit. We also examine effects of the surface on lattice vortices. For the vortex placed parallel to the surface, the increased stability-region feature is also observed, while the vortex cannot exist in a state normal to the surface. More sophisticated localized dynamical structures, such as five-site horseshoes and pyramids, are also considered.

We investigate the process of biopolymer translocation through a narrow pore using a multiscale approach which explicitly accounts for the hydrodynamic interactions of the molecule with the surrounding solvent. The simulations confirm that the coupling of the correlated molecular motion to hydrodynamics results in significant acceleration of the translocation process. Based on these results, we construct a phenomenological model which incorporates the statistical and dynamical features of the translocation process and predicts a power-law dependence of the translocation time on the polymer length with an exponent $\alpha \approx 1.2$. The actual value of the exponent from the simulations is $\alpha =1.28\pm 0.01$, which is in excellent agreement with experimental measurements of DNA translocation through a nanopore, and is not sensitive to the choice of parameters in the simulation. The mechanism behind the emergence of such a robust exponent is related to the interplay between the longitudinal and transversal dynamics of both translocated and untranslocated segments. The connection to the macroscopic picture involves separating the contributions from the blob shrinking and shifting processes, which are both essential to the translocation dynamics.

By using the Wang-Landau flat-histogram Monte Carlo (MC) method for very large lattice sizes never simulated before, we show that the phase transition in the frustrated Heisenberg stacked triangular antiferromagnet is of first order, contrary to results of earlier MC simulations using old-fashioned methods. Our result lends support to the conclusion of a nonperturbative renormalization group performed on an effective Hamiltonian. It puts an end to a $20\text{−}\text{year}$-long controversial issue.

During development, tissues often undergo rapid physical expansion due to cell proliferation. Continuous and discrete models of one- and two-dimensional tissue growth are developed and applied to observational data of the developing avian gut, where the gut tissue cells undergo dramatic proliferation. The discrete cellular automata model provides results at the level of individual cells that reflect a realistic stochasticity and nonuniformity expected in cellular systems. Averaging the discrete results predicts population-level properties of the system, which match those of the continuous model. This dual approach provides an understanding of the interaction between the individual-level and population-level aspects of a developmental growth process. Both models are applied to a case study involving the developing intestinal tract of a quail embryo. A nonuniform growth model accurately predicts the positions of measurable biological landmarks within the growing tissue. Furthermore, the discrete model provides a framework for modeling the interactions between growing tissues and other biological mechanisms, such as cell motility and proliferation on an expanding tissue.

Secondary flows that are absent in Newtonian flows are found for semidilute $\lambda$-DNA solutions in abrupt planar 90° microbends at modest levels of elasticity. Flow visualization and microparticle image velocimetry experiments show that a vortex, which is present in the inner, upstream corner of the bend, grows with increasing Reynolds and Weissenberg number $(9.9\times {10}^{-7}<\mathrm{Re}<3.1\times {10}^{-2},0.41<\mathrm{Wi}<126)$. The vortex growth is quantified as a function of elasticity; at high elasticity, the vortex occupies a significant fraction of the upstream channel and distorts the primary flow. The presence of elastic vortices, in which molecules can become trapped for long times, has implications for the design of microdevices for the processing of biological macromolecules.

We characterize the edge of chaos, the boundary which separates initial conditions which lead to chaotic behavior from those which directly decay to the laminar state, for a nine-dimensional shear flow model. This boundary is the eight-dimensional stable manifold of an unstable periodic orbit, whose properties are characterized. Furthermore, we compute the probability that perturbations of a given energy will lead to transient chaos before decaying to the laminar state, or to a nontrivial attractor for a range of Reynolds numbers. Finally, we consider the relationship between the edge of chaos and linear transient growth, a mechanism which may trigger nonlinear effects that lead to turbulence in shear flows.