An electro-optic oscillator subject to two distinct delayed feedbacks has been designed to develop pronounced broadband chaotic output. Its route to chaos starts with regular pulsating gigahertz oscillations that we investigate both experimentally and theoretically. Of particular physical interest are the transitions to various crenelated fast time-periodic oscillations, prior to the onset of chaotic regimes. The two-delay problem is described mathematically by two coupled delay-differential equations, which we analyze by using multiple-time-scale methods. We show that the interplay of a large delay and a relatively small delay is responsible for the onset of fast oscillations modulated by a slowly varying square-wave envelope. As the bifurcation parameter progressively increases, this envelope undergoes a sequence of bifurcations that corresponds to successive fixed points of a sine map.

The driving parametric regions in frequency-amplitude space and the optimal parameters for single-bubble sonoluminescence (SBSL) in alcohol aqueous solutions are studied systematically by taking measurements of the spectrum and bubble dynamics. The experimental results show that with an increase in alcohol concentration, the region shrinks and shifts. The optimized parameters differ for alcohol solutions having different concentrations, and SBSL driven by fixed parameters dims quickly and is even destroyed immediately with the addition of a small amount of alcohol to pure water. Furthermore, it is seen that the intensity of optimized SBSL decreases as the alcohol concentration increases. The corresponding measurements of the dynamics of the optimized SBSL bubble show that the maximum bubble radius at an alcohol concentration of 1.04 mM is only half that for pure water. Meanwhile, the optimized driving amplitude acquired by direct measurement and that obtained by fitting the radius-time curves with the Rayleigh-Plesset equation both decrease by 12$\%$ in the same comparison. Therefore, a decrease in the driving acoustic pressure may be an important reason for the decrease in the optimized SBSL intensity, which should help clarify SBSL mechanisms in alcohol aqueous solutions.

We analyze a possible extension of Gioia and Chakraborty's momentum transfer model of friction in steady turbulent pipe flows [Phys. Rev. Lett. 96, 044502 (2006)] to the case of time- and/or space-dependent turbulent flows. The end result is an expression for the stress at the wall as the sum of a steady and a dynamic component. The steady part is obtained by using the instantaneous velocity in the expression for the stress at the wall of a stationary flow. The unsteady part is a weighted average over the history of the flow acceleration, with a weighting function similar to that proposed by Vardy and Brown [J. Sound Vibr. 259, 1011 (2003); J. Sound Vibr. 270, 233 (2004)], but naturally including the effect of spatial derivatives of the mean flow, as in the Brunone model [Brunone et al., J. Water Res. Plan. Manage. 126, 236 (2000)].

The present study offers a paradigm on the stability of two-component miscible displacements in a homogeneous porous medium. The components have, in general, different mobility ratios, may diffuse at different rates, and are convected at different speeds. As a result, one of the components may lag behind the other. For the adopted transport models, it is found that the differences in the rates of diffusion and the lag between the two component fronts resulting from the differences in the speeds of convection can modify radically the instability characteristics. In particular, an unstable single-component displacement is always made more unstable by the presence of a second unfavorable component. The instability of the same flow is, on the other hand, attenuated by the presence of a favorable, less diffusive lagging component. However, this same flow instability can actually be enhanced when the favorable lagging second component is more diffusive. Furthermore, the larger the lag between the two components is, the more unstable the flow is when the lagging component is favorable to the displacement. An opposite trend is found when the the lagging component is unfavorable to the displacement. Finally, changes due to the lag between the two components fronts are stronger for a less diffusive lagging component and weaker for a more diffusive one. For illustration, these results are discussed in the special context of a thermal displacement where mass and heat are transported in the porous media.

We numerically investigate the structures of the near-plate temperature profiles close to the bottom and top plates of turbulent Rayleigh-Bénard flow in a cylindrical sample at Rayleigh numbers $\text{Ra}={10}^8$ to $\text{Ra}=2\times {10}^{12}$ and Prandtl numbers $\text{Pr}=6.4$ and $\text{Pr}=0.7$ with the dynamical frame method [Zhou and Xia, Phys. Rev. Lett. 104, 104301 (2010)], thus extending previous results for quasi-two-dimensional systems to three-dimensional systems. The dynamical frame method shows that the measured temperature profiles in the spatially and temporally local frame are much closer to the temperature profile of a laminar, zero-pressure gradient boundary layer (BL) according to Pohlhausen than in the fixed reference frame. The deviation between the measured profiles in the dynamical reference frame and the laminar profiles increases with decreasing Pr, where the thermal BL is more exposed to the bulk fluctuations due to the thinner kinetic BL, and increasing Ra, where more plumes are passing the measurement location.

We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps into boundary layers of finite width. We show that in the limit of vanishing boundary layer width no heat is dissipated in the boundary layer, while work can be done. We further give an alternative interpretation of the fact that the optimal protocols in the overdamped limit are given by optimal deterministic transport (Burgers equation).

High-temperature expansions are presently the only viable approach to the numerical calculation of the higher susceptibilities for the spin and the scalar-field models on high-dimensional lattices. The critical amplitudes of these quantities enter into a sequence of universal amplitude ratios that determine the critical equation of state. We have obtained a substantial extension, through order 24, of the high-temperature expansions of the free energy (in presence of a magnetic field) for the Ising models with spin $s⩾1/2$ and for the lattice scalar-field theory with quartic self-interaction on the simple-cubic and the body-centered-cubic lattices in four, five, and six spatial dimensions. A numerical analysis of the higher susceptibilities obtained from these expansions yields results consistent with the widely accepted ideas, based on the renormalization group and the constructive approach to Euclidean quantum field theory, concerning the no-interaction (“triviality”) property of the continuum (scaling) limit of spin-$s$ Ising and lattice scalar-field models at and above the upper critical dimensionality.

In this paper we study the hard sphere packing problem in the Hamming space by the cavity method. We show that both the replica symmetric and the replica symmetry breaking approximations give maximum rates of packing that are asymptotically the same as the lower bound of Gilbert and Varshamov. Consistently with known numerical results, the replica symmetric equations also suggest a crystalline solution, where for even diameters the spheres are more likely to be found in one of the subspaces (even or odd) of the Hamming space. These crystalline packings can be generated by a recursive algorithm which finds maximum packings in an ultrametric space. Finally, we design a message passing algorithm based on the cavity equations to find dense packings of hard spheres. Known maximum packings are reproduced efficiently in nontrivial ranges of dimensions and number of spheres.

We study the patterns formed by adding $N$ sand grains at a single site on an initial periodic background in the Abelian sandpile models, and relaxing the configuration. When the heights at all sites in the initial background are low enough, one gets patterns showing proportionate growth, with the diameter of the pattern formed growing as $N^{1/d}$ for large $N$, in $d$ dimensions. On the other hand, if sites with maximum stable height in the starting configuration form an infinite cluster, we get avalanches that do not stop. In this paper we describe our unexpected finding of an interesting class of backgrounds in two dimensions that show an intermediate behavior: For any $N$, the avalanches are finite, but the diameter of the pattern increases as $N^{\alpha }$, for large $N$, with $1/2<\alpha ⩽1$. Different values of $\alpha$ can be realized on different backgrounds, and the patterns still show proportionate growth. The noncompact nature of growth simplifies their analysis significantly. We characterize the asymptotic pattern exactly for one illustrative example with $\alpha =1$.

Scalings for slow drag and wall pressures in a plunged granular column are experimentally studied. A granular column is prepared in a cylindrical container and a spherical intruder is slowly plunged into it. Quasistatic drag force and pressures at the bottom and the side wall are measured simultaneously. Using the experimental data, we find scaling laws for drag force and wall pressures with some relevant length scales such as grains size and column dimensions. The obtained scaling laws elucidate the origin of nonlinear behavior of granular pressure. That is, the dimensionless column thickness is a key parameter to characterize the nonlinear granular pressure transmission.

In this paper, we describe the derivation of a model for the simulation of phase transformations in multicomponent real alloys starting from a grand-potential functional. We first point out the limitations of a phase-field model when evolution equations for the concentration and the phase-field variables are derived from a free energy functional. These limitations are mainly attributed to the contribution of the grand-chemical-potential excess to the interface energy. For a range of applications, the magnitude of this excess becomes large and its influence on interface profiles and dynamics is not negligible. The related constraint regarding the choice of the interface thickness limits the size of the domain that can be simulated and, hence, the effect of larger scales on microstructure evolution can not be observed. We propose a modification to the model in order to decouple the bulk and interface contributions. Following this, we perform the thin-interface asymptotic analysis of the phase-field model. Through this, we determine the thin-interface kinetic coefficient and the antitrapping current to remove the chemical potential jump at the interface. We limit our analysis to the Stefan condition at lowest order in $\epsilon$ (parameter related to the interface width) and apply results from previous literature that the corrections to the Stefan condition (surface diffusion and interface stretching) at higher orders are removed when antisymmetric interpolation functions are used for interpolating the grand-potential densities and the diffusion mobilities.

Periodic reversals in the direction of motion in systems of self-propelled rod-shaped bacteria enable them to effectively resolve traffic jams formed during swarming and maximize the swarming rate of the colony. In this paper, a connection is established between a microscopic one-dimensional cell-based stochastic model of reversing nonoverlapping bacteria and a macroscopic nonlinear diffusion equation describing the dynamics of cellular density. Boltzmann-Matano analysis is used to determine the nonlinear diffusion equation corresponding to the specific reversal frequency. Stochastic dynamics averaged over an ensemble is shown to be in very good agreement with the numerical solutions of this nonlinear diffusion equation. Critical density $p_0$ is obtained such that nonlinear diffusion is dominated by the collisions between cells for the densities $p>p_0$. An analytical approximation of the pairwise collision time and semianalytical fit for the total jam time per reversal period are also obtained. It is shown that cell populations with high reversal frequencies are able to spread out effectively at high densities. If the cells rarely reverse, then they are able to spread out at lower densities but are less efficient at spreading out at higher densities.

Many models of disease and rumor-spreading phenomena average the behavior of individuals in a population in order to obtain a coarse description of expected system behavior. For these types of models, we determine how close the coarse approximation is to its corresponding agent-based system. These findings lead to a general result on the logistic behavior of information propagation for networks on both connected graphs with doubly stochastic edge weights, and connected graphs with symmetric edge weights. Moreover, we discuss the appropriateness of the discrete logistic approximation for a few example heterogeneous graph topologies.

We investigate the transition from unidirectional to delayed bidirectional coupling of semiconductor lasers. By tuning the coupling strength in one direction we show how the locking region evolves as a function of the detuning and coupling strength. We consider two representative values of the relaxation oscillation damping: one where the relaxation oscillations are very underdamped and one where they are very overdamped. Qualitatively different dynamical scenarios are shown to emerge for each case. Several features of the delayed bidirectional system can be seen as remaining from the unidirectional system while others clearly arise due to the delayed coupling and are similar to effects seen in delayed feedback configurations.

We study response and velocity autocorrelation functions for a tagged particle in a shear driven suspension governed by underdamped stochastic dynamics. We follow the idea of an effective confinement in dense suspensions and exploit a time scale separation between particle reorganization and vibrational motion. This allows us to approximately derive the fluctuation-dissipation theorem in a “hybrid” form involving the kinetic temperature as an effective temperature and an additive correction term. We show numerically that even in a moderately dense suspension the latter is negligible. We discuss similarities and differences with a simple toy model, a single trapped particle in shear flow.

We establish a general theory of feedback control on classical stochastic thermodynamic systems and generalize nonequilibrium equalities such as the fluctuation theorem and the Jarzynski equality in the presence of feedback control with multiple measurements. Our results are generalizations of the previous relevant works to the situations with general measurements and multiple heat baths. The obtained equalities involve additional terms that characterize the information obtained by measurements or the efficacy of feedback control. A generalized Szilard engine and a feedback-controlled ratchet are shown to satisfy the derived equalities.

We report x-ray photon correlation spectroscopy measurements of advective and diffusive dynamics in a dispersion of colloidal particles subjected to homogeneous shear flow in a rotating-disk shear cell. Intensity autocorrelation functions from scattering data collected using homodyne detection respond to the variation in velocity across the scattering volume when the scattering vector has a component parallel to the flow direction. Theoretical expressions for the impact of homogenous shear flow on the correlation function provide a quantitative prediction of the dependence of correlation functions on the scattering vector and shear rate. Under most circumstances, the applied shear deformation dominates the decay of the intensity correlation function. When scattering data are collected perpendicular to the flow direction, it is possible to measure the diffusive dynamics of the particles free from effects of the superimposed shear flow; however, this approach only works below some upper shear rate limit, beyond which data are affected either by shear effects (caused by the finite width of the detector) or by particle transit through the scattering volume.

Recent experiments have shown the double-stranded (ds) DNAs readily bend and loop over the scale much shorter than their persistence length (50 nm). In an effort to unveil this seemingly surprising phenomenon, we study the emergence of bubbles in short ds DNA loops by simulating the breathing DNA model. We analyze the bubble size distributions and the melting curves for varying contour lengths, which are critically compared with those of linear DNA of the same lengths. We analytically evaluate the free energies associated with double-strand bending and single-strand bubble formation to explain the simulation data. It is found that in shorter looped DNA the bubbles are more easily initiated and formed to release the large bending energy, giving rise to melting at a lower temperature and a lower contour length.

The breakup of small solid aggregates in homogeneous and isotropic turbulence is studied theoretically and by using direct numerical simulations at high Reynolds number, ${\text{Re}}_{\lambda }\simeq 400$. We show that turbulent fluctuations of the hydrodynamic stress along the aggregate trajectory play a key role in determining the aggregate mass distribution function. The differences between turbulent and laminar flows are discussed. A definition of the fragmentation rate is proposed in terms of the typical frequency at which the hydrodynamic stress becomes sufficiently high to cause breakup along each Lagrangian path. We also define an Eulerian proxy of the real fragmentation rate, based on the joint statistics of the stress and its time derivative, which should be easier to measure in any experimental setup. Both our Eulerian and Lagrangian formulations define a clear procedure for the computation of the mass distribution function due to fragmentation. Contrary, previous estimates based only on single point statistics of the hydrodynamic stress exhibit some deficiencies. These are discussed by investigating the evolution of an ensemble of aggregates undergoing breakup and aggregation.