Reaction-diffusion models can exhibit continuous phase transitions in behaviors, and their dynamics at criticality often exhibit scalings with key parameters that can be characterized by exponents. While models with only a single field that transitions between absorbing and nonabsorbing states are well characterized and typically fall in the directed percolation universality class, the effects of coupling multiple fields remain poorly understood. We recently introduced a model which has three fields: one of which relaxes exponentially, one of which displays critical behavior, and one of which has purely diffusive dynamics but exerts an influence on the critical field [Tchernookov et al., J. Chem. Phys. 130, 134906 (2009)]. Simulations suggested that this model is in a universality class distinct from other reaction-diffusion systems studied previously. Although the three fields give rise to interesting physics, they complicate analysis of the model with renormalization-group methods. Here, we show how to systematically simplify the action for this model such that analytical expressions for the exponents of this universality class can be obtained by standard means. We expect the approach taken here to be of general applicability in reaction-diffusion systems with coupled order parameters that display qualitatively different behaviors close to criticality.

Long molecular ligands or “tethers” play an important role in the self-assembly of many nanoscale systems. These tethers, whose only interaction may be a hard-core repulsion, contribute significantly to the free energy of the system because of their large conformational entropy. Here, we investigate how simple approximate models can be developed and used to quickly determine the configurations into which tethers will self assemble in nanoscale systems. We derive criteria that determine when these models are expected to be accurate. Finally, we propose a generalized two-body approximation that can be used as a toy model for the self-assembly of tethers in systems of arbitrary geometry and apply this to the self-assembly of self-assembled monolayers on a planar surface. We compare our results to those in the literature obtained via atomistic and dissipative particle dynamics simulations.

We study the propulsion of a micron-size paramagnetic colloidal doublet dispersed in water and driven above a surface by an external precessing magnetic field. The applied field forces the doublet to precess around an axis parallel to the plane of motion and the rotation of the colloidal assembly is rectified into translation due to a periodic asymmetry in dissipation close to the bounding plate. These recent experimental findings [P. Tierno, R. Golestanian, I. Pagonabarraga, and F. Sagués, Phys. Rev. Lett. 101, 218304 (2008)] are complemented here with a theoretical analysis of the system and extended to more complex magnetic modulations such as elliptical driving fields. Experimental results show a good agreement with numerical simulations with the aim to find the best conditions toward the optimization of propulsion speed and swimming efficiency.

Various aspects of axial banding of size-varying bidisperse granular mixtures in cylindrical tumblers have been documented repeatedly over a decade or so, but the dependence of surface band formation on the relative concentration of particles and rotation rate has not been thoroughly examined. Coarsening patterns analogous to nucleation and spinodal decomposition occur as the relative concentration of small and large particles and the rotation rate of the tumbler are varied. A phase diagram with a portion analogous to a miscibility gap can be constructed from the space-time plots. A dynamic scaling approach similar to that for reacting lamellae can be applied to the coarsening patterns as a result of large bands growing at the expense of neighboring smaller bands.

To identify communities in directed networks, we propose a generalized form of modularity in directed networks by presenting the quantity LinkRank, which can be considered as the PageRank of links. This generalization is consistent with the original modularity in undirected networks and the modularity optimization methods developed for undirected networks can be directly applied to directed networks by optimizing our modified modularity. Also, a model network, which can be used as a benchmark network in further community studies, is proposed to verify our method. Our method is supposed to find communities effectively in citation- or reference-based directed networks.

We propose a method for inferring the existence of hidden common causes from observations of bivariate time series. We detect related time series by excessive simultaneous recurrences in the corresponding recurrence plots. We also use a noncoverage property of a recurrence plot by the other to deny the existence of a directional coupling. We apply the proposed method to real wind data.

The drift behavior of two-armed spirals induced by periodic advective field and periodic modulation of excitability is investigated. It is shown that the two-armed spirals controlled by periodic advective field and periodic modulation of excitability drift in completely different ways. For periodic advective field, the two tips of the two-armed spiral drift in the same direction and the two-armed spiral is stable. While for periodic modulation of excitability, the two tips drift in the opposite direction and the two-armed spiral splits into two single-armed spirals. Analytical results based on a kinematic theory of rotating spirals in weakly excitable media are consistent with the numerical results.

Analytical investigations are carried out on pulsating laminar incompressible fully developed channel and pipe flows. An analytical solution of the velocity profile for arbitrary time-periodic pulsations is derived by approximating the pulsating flow variables by a Fourier series. The explicit interdependence between pulsations of velocity, mass-flow rate, pressure gradient, and wall shear stress are shown by using the proper dimensionless parameters that govern the flow. Utilizing the analytical results, the scaling laws for dimensionless pulsation amplitudes of the velocity, mass-flow rate, pressure gradient, and wall shear stress are analyzed as functions of the dimensionless pulsation frequency. Special attention has been given to the scaling laws describing the flow reversal phenomenon occurring in pulsating flows, such as the condition for flow reversal, the dependency of the reversal duration, and the amplitude. It is shown that two reversal locations away from the wall can occur in pulsating flows in pipes and channels and the reversed amount of mass per period reaches a maximum at a certain dimensionless frequency for a given amplitude of mass-flow rate fluctuations. These analyses are numerically conducted for pipe and channel flows over a large frequency range in a comparative manner.

We present a systematic analytical study of the dynamics of nonlinear magnetoinductive waves in a one-dimensional diatomic lattice of split ring resonators (SRRs) with Kerr nonlinear interaction between nearest neighbors. The linear spectrum of this model have two branches and exhibits a gap, which is proportional to the difference between two types of SRRs. We analyze the nonlinear excitations genuine of the discreteness and nonlinearity in such a diatomic chain based on an extended quasidiscreteness approach. Gap solitons (with vibrating frequency lying in the gap), resonant kinks (with the vibrating frequency lying in the frequency bands), and intrinsic localized modes (with the vibrating frequency being above all the frequency bands) are obtained explicitly. It is also shown that the existence of different localized structures depend strongly on the type of nonlinearity of the embedded medium (a self-focusing or defocusing one).

We have experimentally and theoretically studied the interparticle force between two colloidal particles with different sizes accompanied by hyperbolic hedgehog defects in a nematic liquid crystal. The force $f$ was directly measured using dual-beam optical tweezers and calculated theoretically from the equilibrium tensor field around the particles. The dependence of $f$ on the center-to-center distance between particles of different sizes $R$ is different from that for particles with the same size. The magnitude of $f$ depends on the relative arrangement of the particles: $f$ is larger when a defect between the particles belongs to the larger particle. From the theoretical calculation, the difference in $f$ between the two arrangements, $\delta f$, monotonically increases with increasing size difference. The difference $\delta f$ was experimentally and theoretically found to be proportional to $R^{-4.6}$ at large $R$. The obtained exponent is comparable to the exponent of $-5$ predicted by electrostatic analogy.

We consider an isolated macroscopic quantum system. Let $\mathcal{H}$ be a microcanonical “energy shell,” i.e., a subspace of the system’s Hilbert space spanned by the (finitely) many energy eigenstates with energies between $E$ and $E+\delta E$. The thermal equilibrium macrostate at energy $E$ corresponds to a subspace ${\mathcal{H}}_{eq}$ of $\mathcal{H}$ such that $\text{dim}{\mathcal{H}}_{eq}/\text{dim}\mathcal{H}$ is close to 1. We say that a system with state vector $\psi ∊\mathcal{H}$ is in thermal equilibrium if $\psi$ is “close” to ${\mathcal{H}}_{eq}$. We show that for “typical” Hamiltonians with given eigenvalues, all initial state vectors ${\psi }_0$ evolve in such a way that ${\psi }_t$ is in thermal equilibrium for most times $t$. This result is closely related to von Neumann’s quantum ergodic theorem of 1929.

Amplitude representations of a binary phase-field-crystal model are developed for a two-dimensional triangular lattice and three-dimensional bcc and fcc crystal structures. The relationship between these amplitude equations and the standard phase-field models for binary-alloy solidification with elasticity are derived, providing an explicit connection between phase-field-crystal and phase-field models. Sample simulations of solute migration at grain boundaries, eutectic solidification, and quantum dot formation on nanomembranes are also presented.

Plane Couette flow, the flow between two parallel plates moving in opposite directions, belongs to the group of shear flows where turbulence occurs while the laminar profile is stable. Experimental and numerical studies show that at intermediate Reynolds numbers turbulence is transient and that the lifetimes are distributed exponentially. However, these studies have remained inconclusive about a divergence in lifetimes above a critical Reynolds number. The extensive numerical results for flow in a box of width 2π and length 8π presented here cover observation times up to $12000$ units and show that while the lifetimes increase rapidly with Reynolds number, they do not indicate a divergence and therefore no transition to persistent turbulence.

Molecular dynamics simulations are used to study contact between a rigid, nonadhesive, and spherical tip with radius of order 30 nm and a flat elastic substrate covered with a fluid monolayer of adsorbed chain molecules. Previous studies of bare surfaces showed that the atomic scale deviations from a sphere that are present on any tip constructed from discrete atoms lead to significant deviations from continuum theory and dramatic variability in friction forces. Introducing an adsorbed monolayer leads to larger deviations from continuum theory but decreases the variations between tips with different atomic structure. Although the film is fluid, it remains in the contact and behaves qualitatively like a thin elastic coating except for certain tips at high loads. Measures of the contact area based on the moments or outer limits of the pressure distribution and on counting contacting atoms are compared. The number of tip atoms making contact during a time interval $\Delta t$ grows as a power of $\Delta t$ when the film is present and as the logarithm of $\Delta t$ for bare surfaces. Friction is measured by displacing the tip at a constant velocity or pulling the tip with a spring. Both static and kinetic friction rise linearly with load at small loads. Transitions in the state of the film lead to nonlinear behavior at large loads. The friction is less clearly correlated with contact area than load.

We study the spatiotemporal dynamics of the Hamiltonian four-wave interaction in its counterpropagating configuration. The numerical simulations reveal that, under rather general conditions, the four-wave system exhibits a relaxation process toward a stationary state. Considering the Hamiltonian system associated to the stationary state, we provide a global geometrical view of all the stationary solutions of the system. The analysis reveals that the stationary state converges exponentially toward a pinched torus of the Hamiltonian system in the limit of an infinite nonlinear medium. The singular torus thus plays the role of an attractor for the spatiotemporal wave system. The topological properties of the singular torus confer a robust character to the stationary solution when the boundary conditions or the length of the nonlinear medium are modified. Furthermore, an adiabatic approach of the boundary conditions reveals that singular tori also play a major role for the description of the spatiotemporal dynamics of the wave system.

Low-energy non-neutral electron plasmas were confined with an electrostatic potential and a magnetic mirror field of the mirror ratio up to 5. Using a conventional phosphor screen and the unique multiring trap, both radial and axial density profiles of plasmas were measured. With the present experimental parameters, it was confirmed that a plasma density increased at higher field with an electrostatic confinement and that it decreased at higher field with a magnetic mirror confinement. The electrostatic potentials along the magnetic field were estimated with computer simulations.

We discuss theoretically the Goos-Hänchen (GH) shifts of the reflected waves from a cold, inhomogeneous, and magnetized plasma slab by using the invariant imbedding approach. Aiming at the linear and parabolic electron-density profiles, we demonstrate numerically the dependences of the co- and cross-polarized GH shifts on the angle of incidence, external static magnetic field, and the thickness of the plasma slab. The results show that the different electron-density profiles of plasma can result in the very different dependences of the GH shifts on the angle of incidence, external magnetic field, and the slab’s thickness; the GH shifts can be switched between the considerably large positive and negative values under certain conditions. Particularly, without altering the structure of the plasma slab, the GH shifts can be manipulated by modifying the angle of incident or the external static magnetic field.

We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing–Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs.

We consider a model system in which anomalous diffusion is generated by superposition of underlying linear modes with a broad range of relaxation times. In the language of Gaussian polymers, our model corresponds to Rouse (Fourier) modes whose friction coefficients scale as wave number to the power $2-z$. A single (tagged) monomer then executes subdiffusion over a broad range of time scales, and its mean square displacement increases as $t^{\alpha }$ with $\alpha =1/z$. To demonstrate nontrivial aspects of the model, we numerically study the absorption of the tagged particle in one dimension near an absorbing boundary or in the interval between two such boundaries. We obtain absorption probability densities as a function of time, as well as the position-dependent distribution for unabsorbed particles, at several values of $\alpha$. Each of these properties has features characterized by exponents that depend on $\alpha$. Characteristic distributions found for different values of $\alpha$ have similar qualitative features, but are not simply related quantitatively. Comparison of the motion of translocation coordinate of a polymer moving through a pore in a membrane with the diffusing tagged monomer with identical $\alpha$ also reveals quantitative differences.

Linear response functions of aging systems are routinely interpreted using the scaling variable $t_{\text{obs}}/t_w^{\mu }$, where $t_w$ is the time at which the field conjugated to the response is turned on or off, and where $t_{\text{obs}}$ is the “observation” time elapsed from the field change. The response curve obtained for different values of $t_w$ are usually collapsed using values of $\mu$ slightly below one, a scaling behavior generally known as subaging. Recent spin glass thermoremanent magnetization experiments have shown that the value of $\mu$ is strongly affected by the form of the initial cooling protocol [G. F. Rodriguez et al., Phys. Rev. Lett. 91, 037203 (2003)], and even more importantly [G. G. Kenning et al., Phys. Rev. Lett. 97, 057201 (2006)], that the $t_w$ dependence of the response curves vanishes altogether in the limit $t_{\text{obs}}⪢t_w$. The latter result shows that $t_{\text{obs}}/t_w^{\mu }$ scaling of linear response data cannot be generally valid, thereby casting some doubt on the theoretical significance of the exponent $\mu$. In this work, a common mechanism is proposed for the origin of both subaging and end of aging behavior in glassy dynamics. The mechanism combines real and configuration space properties of the state produced by the initial thermal quench which initiates the aging process.