Using a combination of experimental results acquired through positron emission particle tracking and simulational results obtained via the discrete particle method, we determine a scaling relationship for the center of mass height of a vibrofluidized three-dimensional, bidisperse granular system. We find the scaling to be dependent on the characteristic velocity with which the system is driven, the depth of the granular bed, and the elasticities of the particles involved, as well as the degree of segregation exhibited by the system and the ratio of masses between particle species. The scaling is observed to be robust over a significant range of system parameters.

In this paper we consider a physical system in which two DNA molecules braid about each other. The distance between the two molecular ends, on either side of the braid, is held at a distance much larger than supercoiling radius of the braid. The system is subjected to an external pulling force, and a moment that induces the braiding. In a model, developed for understanding such a system, we assume that each molecule can be divided into a braided and unbraided section. We also suppose that the DNA is nicked so that there is no constraint of the individual linking numbers of the molecules. Included in the model are steric and electrostatic interactions, thermal fluctuations of the braided and unbraided sections of the molecule, as well as the constraint on the braid linking (catenation) number. We compare two approximations used in estimating the free energy of the braided section. One is where the amplitude of undulations of one molecule with respect to the other is determined only by steric interactions. The other is a self-consistent determination of the mean-squared amplitude of these undulations. In this second approximation electrostatics should play an important role in determining this quantity, as suggested by physical arguments. We see that if the electrostatic interaction is sufficiently large there are indeed notable differences between the two approximations. We go on to test the self-consistent approximation—included in the full model—against experimental data for such a system, and we find good agreement. However, there seems to be a slight left-right-handed braid asymmetry in some of the experimental results. We discuss what might be the origin of this small asymmetry.

A fundamental understanding of cell-nanomaterial interaction is essential for biomedical diagnostics, therapeutics, and nanotoxicity. Here, we perform a theoretical analysis to investigate the phase diagram and morphological evolution of an elastic rod-shaped nanoparticle wrapped by a lipid membrane in two dimensions. We show that there exist five possible wrapping phases based on the stability of full wrapping, partial wrapping, and no wrapping states. The wrapping phases depend on the shape and size of the particle, adhesion energy, membrane tension, and bending rigidity ratio between the particle and membrane. While symmetric morphologies are observed in the early and late stages of wrapping, in between a soft rod-shaped nanoparticle undergoes a dramatic symmetry breaking morphological change while stiff and rigid nanoparticles experience a sharp reorientation. These results are of interest to the study of a range of phenomena including viral budding, exocytosis, as well as endocytosis or phagocytosis of elastic particles into cells.

We study explosive synchronization, a phenomenon characterized by first-order phase transitions between incoherent and synchronized states in networks of coupled oscillators. While explosive synchronization has been the subject of many recent studies, in each case strong conditions on the heterogeneity of the network, its link weights, or its initial construction are imposed to engineer a first-order phase transition. This raises the question of how robust explosive synchronization is in view of more realistic structural and dynamical properties. Here we show that explosive synchronization can be induced in mildly heterogeneous networks by the addition of quenched disorder to the oscillators' frequencies, demonstrating that it is not only robust to, but moreover promoted by, this natural mechanism. We support these findings with numerical and analytical results, presenting simulations of a real neural network as well as a self-consistency theory used to study synthetic networks.

We study condensation in one-dimensional transport models with a kinetic constraint. The kinetic constraint results in clustering of immobile vehicles; these clusters can grow to macroscopic condensates, indicating the onset of dynamic phase separation between free-flowing and arrested traffic. We investigate analytically the conditions under which this occurs and derive a necessary and sufficient criterion for phase separation. This criterion is applied to the well-known Nagel-Schreckenberg model of traffic flow to analytically investigate the existence of dynamic condensates. We find that true condensates occur only when acceleration out of jammed traffic happens in a single time step, in the limit of strong overbraking. Our predictions are further verified with simulation results on the growth of arrested clusters. These results provide analytic understanding of dynamic arrest and dynamic phase separation in one-dimensional traffic and transport models.

The geometric orientation of the subfilter-scale scalar-flux vector is examined in homogeneous isotropic turbulence. Vector orientation is determined using the eigenframe of the resolved strain-rate tensor. The Schmidt number is kept sufficiently large so as to leave the velocity field, and hence the strain-rate tensor, unaltered by filtering in the viscous-convective subrange. Strong preferential alignment is observed for the case of Gaussian and box filters, whereas the sharp-spectral filter leads to close to a random orientation. The orientation angle obtained with the Gaussian and box filters is largely independent of the filter width and the Schmidt number. It is shown that the alignment direction observed numerically using these two filters is predicted very well by the tensor-diffusivity model. Moreover, preferred alignment of the scalar gradient vector in the eigenframe is shown to mitigate any probable issues of negative diffusivity in the tensor-diffusivity model. Consequentially, the model might not suffer from solution instability when used for large eddy simulations of scalar transport in homogeneous isotropic turbulence. Further a priori tests indicate poor alignment of the Smagorinsky and stretched vortex model predictions with the exact subfilter flux. Finally, strong filter dependence of subfilter scalar-flux orientation suggests that explicit filtering may be preferable to implicit filtering in large eddy simulations.

We numerically investigate the saturation of the hydromagnetic instabilities of a magnetized spherical Couette flow. Previous simulations demonstrated a region where the axisymmetric flow, calculated from a 2D simulation, was linearly unstable to nonaxisymmetric perturbations. Full, nonlinear, 3d simulations showed that the saturated state would consist only of harmonics of one azimuthal wave number, though there were bifurcations and transitions as nondimensional parameters (Re, Ha) were varied. Here, the energy transfer between different azimuthal modes is formulated as a network. This demonstrates a mechanism for the saturation of one mode and for the suppression of other unstable modes. A given mode grows by extracting energy from the axisymmetric flow, and then saturates as the energy transfer to its second harmonic equals this inflow. At the same time, this mode suppresses other unstable modes by facilitating an energy transfer to linearly stable modes.

Starting from our recent chemical master equation derivation of the model of an autocatalytic reaction-diffusion chemical system with reactions $U+2V\stackrel{{\lambda }_0}{\to }3V$ and $V\stackrel{\mu }{\to }P$, $U\stackrel{\nu }{\to }Q$, we determine the effects of intrinsic noise on the momentum-space behavior of its kinetic parameters and chemical concentrations. We demonstrate that the intrinsic noise induces $n\to n$ molecular interaction processes with $n\ge 4$, where $n$ is the number of participating molecules of type $U$ or $V$. The momentum dependences of the reaction rates are driven by the fact that the autocatalytic reaction (inelastic scattering) is renormalized through the existence of an arbitrary number of intermediate elastic scatterings, which can also be interpreted as the creation and subsequent decay of a three body composite state $\sigma ={\varphi }_u{\varphi }_v^2$, where ${\varphi }_i$ corresponds to the fields representing the densities of $U$ and $V$. Finally, we discuss the difference between representing $\sigma$ as a composite or an elementary particle (molecule) with its own kinetic parameters. In one dimension, we find that while they show markedly different behavior in the short spatiotemporal scale, high-momentum (UV) limit, they are formally equivalent in the large spatiotemporal scale, low momentum (IR) regime. On the other hand, in two dimensions and greater, due to the effects of fluctuations, there is no way to experimentally distinguish between a fundamental and composite $\sigma$. Thus, in this regime, $\sigma$ behaves as an entity unto itself, suggesting that it can be effectively treated as an independent chemical species.

The cover time is defined as the time needed for a random walker to visit every site of a confined domain. Here, we focus on persistent random walks, which provide a minimal model of random walks with short-range memory. We derive the exact expression of the mean cover time of a one-dimensional lattice by such a persistent random walk, both for periodic and reflecting boundary conditions.

We have performed a three-dimensional simulation of mesoscopic structures in a mixture of $\mathrm{AB}$ amphiphilic molecule and $C$ solvent by employing the density-functional theory under the conditions that (i) the size of the $\mathrm{AB}$ is much larger than $C$ and (ii) the affinity between $A$ and $B$ is much larger than the affinity between $B$ and $C$. First, we have calculated the free energy of five periodic structures, i.e., the lamellar phase, hexagonally packed cylinders, body-centered-cubic spheres, face-centered-cubic spheres, and gyroid phase for different sets of the concentration of $\mathrm{AB}$ (${\overline{\varphi }}_{AB}$) and the $\chi$ parameter (${\chi }_{AC}$). By comparing the free energies for these structures, the ${\chi }_{AC}$-${\overline{\varphi }}_{AB}$ phase diagram has been obtained. In addition to these periodic structures, it has been shown that nonperiodic structures such as spherical and rodlike micelles can be obtained although they might be metastable phase.

We use simulations of a binary polymer blend confined between selectively attracting walls to identify and explain the mechanism of lateral phase separation via a transient wetting layer. We first show that equilibrium phases in the film are described by one-dimensional phase equilibria in the vertical (depth) dimension, and demonstrate that effective boundary conditions imposed by the film walls pin the film profile at the walls. We then show that, prior to lateral phase separation, distortion of the interface in a transient wetting layer is coupled to lateral phase separation at the walls. Using Hamiltonian phase portraits, we explain a “surface bifurcation mechanism” whereby the volume fraction at the walls evolves and controls the dynamics of the phase separation. We suggest how solvent evaporation may assist our mechanism.

Models that invoke nonlinear wavefront propagation in a chemically excitable medium are rife in the biological literature. Indeed, the idea that wavefront propagation can serve as a signaling mechanism has often been invoked to explain synchronization of developmental processes. In this paper we suggest a kind of signaling based not on diffusion of a chemical species but on the propagation of mechanical stress. We construct a theoretical approach to describe mechanical signaling as a nonlinear wavefront propagation problem and study its dependence on key variables such as the effective elasticity and damping of the medium.

Slow coherent spontaneous fluctuations ($<$0.1 Hz) in functional magnetic resonance imaging blood-oxygen-level-dependent signals have been observed for a resting state of the human brain. In this paper, considering feed-forward inhibition in addition to excitation between brain areas, which we assume to be in up (active) or down (quiescent) states, we propose a model for the generation and organization of the slow fluctuations. Connectivity with feed-forward excitation and inhibition between the areas makes the system have multiple stable states and organized slow fluctuations manifest as noise-induced slow transitions between the states. With various connectivities, we observe slow fluctuations and various organizations, including anticorrelated clusters, through numerical simulations.

This paper comprises numerical and theoretical studies of spatiotemporal patterns in advection-reaction-diffusion systems in which the chemical species interact with the hydrodynamic fluid. Due to the interplay between the two, we obtained the spiral defect chaos in the activator-inhibitor-type model. We formulated the generalized Swift-Hohenberg-type model for this system. Then the evolution of fractal boundaries due to the effect of the strong nonlinearity at the interface of the two chemical species is studied numerically. The purpose of the present paper is to point out that spiral defect chaos, observed in model equations of the extended Swift-Hohenberg equation for low Prandtl number convection, may actually be obtained also in certain advection-reaction-diffusion systems.

We analyze both experimentally and numerically the formation of microbubbles in the jetting regime reached when a moderately viscous liquid stream focuses a gaseous meniscus inside a converging micronozzle. If the total (stagnation) pressure of the injected gas current is fixed upstream, then there are certain conditions on which a quasisteady gas meniscus forms. The meniscus tip is sharpened by the liquid stream down to the gas molecular scale. On the other side, monodisperse collections of microbubbles can be steadily produced in the jetting regime if the feeding capillary is appropriately located inside the nozzle. In this case, the microbubble size depends on the feeding capillary position. The numerical simulations for an imposed gas flow rate show that a recirculation cell appears in the gaseous meniscus for low enough values of that parameter. The experiments allow one to conclude that the bubble pinch-off comprises two phases: (i) a stretching motion of the precursor jet where the neck radius versus the time before the pinch essentially follows a potential law, and (ii) a final stage where a very thin and slender gaseous thread forms and eventually breaks apart into a number of micron-sized bubbles. Because of the difference between the free surface and core velocities, the gaseous jet breakage differs substantially from that of liquid capillary jets and gives rise to bubbles with diameters much larger than those expected from the Rayleigh-type capillary instability. The dependency of the bubble diameter upon the flow-rate ratio agrees with the scaling law derived by A. M. Gañán-Calvo [Phys. Rev. E 69, 027301 (2004)], although a slight influence of the Reynolds number can be observed in our experiments.

Rayleigh-Bénard convection is investigated in rotating annular cavities at a moderate dimensionless rotation rate $\Omega =60$. The onset of convection is in the form of azimuthal traveling waves that set in at the sidewalls and at values of the Rayleigh number significantly below the value of the onset of convection in an infinitely extended layer. The present study addresses the effects of curvature and confinement on the onset of sidewall convection by using three-dimensional spectral solutions of the Oberbeck-Boussinesq equations. Such solutions demonstrate that the curvature of the outer boundary promotes the onset of the wall mode, while the opposite curvature of the inner boundary tends to delay the onset of the wall mode. An inner sidewall with a radius as low as one tenth of its height is sufficient, however, to support the onset of a sidewall mode. When radial confinement is increased the two independent traveling waves interact and eventually merge to form a nearly steady pattern of convection.

The influence of localized water currents on the nonlinear dynamics and stability of large amplitude, statistically distributed gravity waves is investigated theoretically and numerically by means of an evolution equation for a Wigner function governing the spectrum of waves. It is shown that water waves propagating in the opposite direction of a localized current channel can be trapped in the channel, which can lead to the amplification of the wave intensity. Under certain conditions the wave intensity can be further localized due to a self-focusing (Benjamin-Feir) instability. The localized amplification of the wave intensity may increase the probability of extreme events in the form of freak waves, which have been observed in connection with ocean currents.

We note that extreme multistability of the type described in the referenced paper can be achieved in virtually any dynamical system by adding extraneous variables and using their initial conditions in place of the existing parameters or as additional parameters. We show several simple examples of this and show how the referenced examples are similar.

In this Reply we answer the two major issues raised by the Comment. First, we point out that the idea of constructing extreme multistability in simple dynamical systems is not new and has been demonstrated previously by other authors. Furthermore, we emphasize the importance of the concept of a conserved quantity and its consequences for the dynamics, which applies to all the examples in the Comment. Second, we show that the design of controllers to achieve extreme multistability in coupled systems is as general as described in Phys. Rev. E 85, 035202(R) (2012) by providing two examples which do not lead to a master-slave dynamics.