We consider here a model previously introduced to describe the collective behavior of an ensemble of cold atoms interacting with a coherent electromagnetic field. The atomic motion along the self-generated spatially periodic force field can be interpreted as the rotation of a phase oscillator. This suggests a relationship with synchronization transitions occurring in globally coupled rotators. In fact, we show that whenever the field dynamics can be adiabatically eliminated, the model reduces to a self-consistent equation for the probability distribution of the atomic “phases.” In this limit, there exists a formal equivalence with the Kuramoto model, though with important differences in the self-consistency conditions. Depending on the field-cavity detuning, we show that the onset of synchronized behavior may occur through either a first- or second-order phase transition. Furthermore, we find a secondary threshold, above which a periodic self-pulsing regime sets in, that is immediately followed by the unlocking of the forward-field frequency. At yet higher, but still experimentally meaningful, input intensities, irregular, chaotic oscillations may eventually appear. Finally, we derive a simpler model, involving only five scalar variables, which is able to reproduce the entire phenomenology exhibited by the original model.

In this paper we study how to avoid escapes in open dynamical systems in the presence of dissipation and forcing, as it occurs in realistic physical situations. We use as a prototype model the Helmholtz oscillator, which is the simplest nonlinear oscillator with escapes. For some parameter values, this oscillator presents a critical value of the forcing for which all particles escape from its single well. By using the phase control technique, weakly changing the shape of the potential via a periodic perturbation of suitable phase $\varphi$, we avoid the escapes in different regions of the phase space. We provide numerical evidence, heuristic arguments, and an experimental implementation in an electronic circuit of this phenomenon. Finally, we expect that this method might be useful for avoiding escapes in more complicated physical situations.

Tunneling of microwaves through a smooth barrier in a transmission line is considered. In contrast to standard wave barriers, we study the case where the dielectric permittivity is positive, and the barrier is caused by the inhomogeneous dielectric profile. It is found that reflectionless, superluminal tunneling can take place for waves with a finite spectral width. The consequences of these findings are discussed, and an experimental setup testing our predictions is proposed.

Particles that are embedded in fluid membranes or plates can induce bending if they impose a nonzero angle of contact. This bending mediates complicated effective particle-particle interactions. In the absence of tension, these interactions are nonpairwise additive and can result in clusters of particles with specific configurations that give rise to zero total membrane bending energy. Here, we consider an infinite periodic lattice of such membrane inclusions. Upon summing the nonpairwise interactions within a regular lattice, we find an unexpected infinite number of periodic lattices that preserve zero membrane bending energy. Elliptically shaped membrane inclusions further increase the phase space of this degeneracy.

We analyze traveling solitary wave solutions in the Barbi-Cocco-Peyrard twist-opening model of nonlinear DNA dynamics. We identify conditions, involving an interplay of physical parameters and asymptotic behavior, for such solutions to exist, and provide first-order ordinary differential equations whose solutions give the required solitary waves; these are not solvable in analytical terms, but are easily integrated numerically. The conditions for existence of solitary waves are not satisfied for trivial asymptotic behavior and physical values of the parameters, i.e., the Barbi-Cocco-Peyrard model admits only solitary wave solutions that entail a global modification of the molecule; this is compared with the situation met in another recently formulated class of DNA models with two degrees of freedom per site.

Lakatos et al. [Phys. Rev. E 71, 011103 (2005)] have studied a totally asymmetric exclusion process that contains periodically varying movement rates. They have presented a cluster mean-field theory for the problem. We show that their cluster mean-field theory leads to redundant equations. We present a mean-field analysis in which there is no redundant equation.

We present simulations of coherent structures in compressible flows near the transition to turbulence using the dissipative particle dynamics method. The structures we find are remarkably consistent with experimental observations and direct numerical simulations (DNS) simulations of incompressible flows, despite a difference in Mach number of several orders of magnitude. The bifurcation from the laminar flow is bistable and shifts to higher Reynolds numbers when the fluid becomes more compressible. This work underlines the robustness of coherent structures in the transition to turbulence and illustrates the ability of particle-based methods to reproduce complex nonlinear instabilities.

Spontaneous breakup of propagating waves was investigated in this paper with a ferroin-catalyzed Belousov-Zhabotinsky reaction modified with the inclusion of a second substrate, 1,4-cyclohexanedione (CHD). The presence of CHD, which forms a separate chemical oscillator with acidic bromate, led to the development of a scattered unexcitable regime in the studied medium, where as waves passed through these unexcitable media, the propagation was disrupted, causing the creation of free ends. It thus presents a new avenue through which a chemical wave breaks up to form spirals. By manipulating the concentrations of CHD, sulfuric acid, and bromate, unexcitable regimes of different sizes with different survival times were obtained. Kinetic data on wave speed prior to and after the unexcitable window illustrates that the occurrence of an unexcitable regime is not due to depletion of components needed for wave propagation.

We have investigated a simple coevolutionary network model incorporating three processes—changes of opinions, homophily, and heterophily. In this model, each node holds one of $G$ opinions and changes its opinion, as in the voter model. Homophily is the tendency for connections to form between individuals of the same opinions and heterophily is the opposite effect. If there is no heterophily, this model corresponds to the Holme and Newman model [Phys. Rev. E 74, 056108 (2006)]. We show that the behavior of this model without heterophily can be understood in terms of a mean field approximation. We also find that this model with heterophily exhibits topologically complicated behaviors such as the small-world property.

Rotation and shear flows are ubiquitous features of many astrophysical and geophysical bodies. To understand their origin and effect on turbulent transport in these systems, we consider a forced turbulence and investigate the combined effect of rotation and shear flow on the turbulence properties. Specifically, we study how rotation and flow shear influence the generation of shear flow (e.g., the direction of energy cascade), turbulence level, transport of particles and momentum, and the anisotropy in these quantities. In all the cases considered, turbulence amplitude is always quenched due to strong shear ($\xi =\nu k_y^2/\mathcal{A}⪡1$, where $\mathcal{A}$ is the shearing rate, $\nu$ is the molecular viscosity, and $k_y$ is a characteristic wave number of small-scale turbulence), with stronger reduction in the direction of the shear than those in the perpendicular directions. Specifically, in the large rotation limit $\left(\Omega ⪢\mathcal{A}\right)$, they scale as ${\mathcal{A}}^{-1}$ and ${\mathcal{A}}^{-1}\left|\text{ln}\xi \right|$, respectively, while in the weak rotation limit $\left(\Omega ⪡\mathcal{A}\right)$, they scale as ${\mathcal{A}}^{-1}$ and ${\mathcal{A}}^{-2/3}$, respectively. Thus, flow shear always leads to weak turbulence with an effectively stronger turbulence in the plane perpendicular to shear than in the shear direction, regardless of rotation rate. The anisotropy in turbulence amplitude is, however, weaker by a factor of ${\xi }^{1/3}\left|\text{ln}\xi \right|$ $\left(\propto {\mathcal{A}}^{-1/3}\left|\text{ln}\xi \right|\right)$ in the rapid rotation limit $\left(\Omega ⪢\mathcal{A}\right)$ than that in the weak rotation limit $\left(\Omega ⪡\mathcal{A}\right)$ since rotation favors almost-isotropic turbulence. Compared to turbulence amplitude, particle transport is found to crucially depend on whether rotation is stronger or weaker than flow shear. When rotation is stronger than flow shear $\left(\Omega ⪢\mathcal{A}\right)$, the transport is inhibited by inertial waves, being quenched inversely proportional to the rotation rate (i.e., $\propto {\Omega }^{-1}$) while in the opposite case, it is reduced by shearing as ${\mathcal{A}}^{-1}$. Furthermore, the anisotropy is found to be very weak in the strong rotation limit (by a factor of 2) while significant in the strong shear limit. The turbulent viscosity is found to be negative with inverse cascade of energy as long as rotation is sufficiently strong compared to flow shear $\left(\Omega ⪢A\right)$ while positive in the opposite limit of weak rotation $\left(\Omega ⪡\mathcal{A}\right)$. Even if the eddy viscosity is negative for strong rotation $\left(\Omega ⪢\mathcal{A}\right)$, flow shear, which transfers energy to small scales, has an interesting effect by slowing down the rate of inverse cascade with the value of negative eddy viscosity decreasing as $\left|{\nu }_T\right|\propto {\mathcal{A}}^{-2}$ for strong shear. Furthermore, the interaction between the shear and the rotation is shown to give rise to a nondiffusive flux of angular momentum ($\Lambda$ effect), even in the absence of external sources of anisotropy. This effect provides a mechanism for the existence of shearing structures in astrophysical and geophysical systems.

This study deals with the observation of sand ripples in a circular geometry under oscillatory flow. We characterize the observed patterns as a function of the excitation parameters. We report the time evolution of the corrugated front invading the flat bed. These experiments reveal unambiguously, because of the gradient of shear stress, the existence of two separated thresholds: one for grain motion and the other for the appearance of ripples. In addition, we display the phase diagram of this instability as a function of the Froude number and a Reynolds number.

The first passage times for enzymatic turnovers in nonequilibrium steady state display a statistical symmetry property related to nonequilibrium fluctuation theorems, which makes it possible to extract the chemical driving force from single molecule trajectories in nonequilibrium steady state. Below, we show that the number of decay constants needed to describe the first passage time distribution of this system is not equal to the number of states in the first passage problem, as one would generally expect. Instead, the structure of the kinetic mechanism makes half of the decay times vanish identically from the turnover time distribution. The terms that cancel out correspond to the eigenvalues of a certain submatrix of the master equation matrix for the first exit time problem. We discuss how these results make modeling and data analysis easier for such systems, and how the turnovers can be measured.

We study the motion of a dimer in a one-dimensional spatially periodic washboard potential. The tilt of the latter is time-periodically modulated by an ac field. We focus interest on the detrapping of the (static) ground state solution of the dimer caused by the ac field. Moreover, we demonstrate that slow tilt modulations not only induce a trapping-detrapping transition but drive the dimer dynamics into a regime of transient long-range running states. Most strikingly, the motion proceeds then unidirectionally, so that the dimer covers huge distances regardless of the fact that the bias force in the driven system vanishes on the average. We elucidate the underlying dynamics in phase space and associate long-lasting running states with the motion in ballistic channels occurring due to stickiness to invariant tori.

Application of polymer scaling to the problem of Tolman’s length, a curvature correction coefficient in the interfacial tension, shows that Tolman’s length in polymer solutions may become as large as half of the thickness of the interface. Tolman’s length depends on the degree of polymerization $N$ and the distance to the critical point of phase separation, $\Delta \widehat{T}$. In the “critical” regime $\left(N^{1/2}\left|\Delta \widehat{T}\right|⪡1\right)$ Tolman’s length diverges upon approach to the critical temperature as $\sim N^{0.348}{\left|\Delta \widehat{T}\right|}^{-0.304}$. In the “polymer” regime $\left(N^{1/2}\left|\Delta \widehat{T}\right|⪢1\right)$ Tolman’s length does not depend on $N$, but diverges more strongly, as $\sim {\left|\Delta \widehat{T}\right|}^{-1}$, proportional to the thickness of the interface.

The flexible chainlike walker (FCW) model is proposed as a minimal model of a deformable moving object and as an extension of the regular random-walk model. The many-body system of FCWs is studied by numerical simulations on a square lattice. It is shown that FCWs aggregate spontaneously and irreversibly where no adherence is assumed, in contrast to the established aggregation models, where adherence is indispensable for their occurrence and irreversibility. This type of aggregation is enabled by and demonstrates the significance of the deformability of moving objects.

By different coarse-graining procedures, we derive lower bounds on the total mean work dissipated in Brownian systems driven out of equilibrium. With several analytically solvable examples, we illustrate how, when, and where the information on the dissipation is captured.

We present a study of sediment transport in the creeping and saltation regimes. In our model, a bed of particles is simulated with the conventional event-driven method. The particles are considered as hard disks in a two-dimensional domain with periodic boundary conditions in the horizontal direction. The flow of the fluid over this bed of particles is modeled by imposing a force on each particle that depends on the velocity of the fluid at its height above the bed. We consider two velocity profiles for the fluid, parabolic and logarithmic. The first one models laminar flow and the second corresponds to turbulent flow. For each case we investigate the behavior of the saturated flux. We find that for the logarithmic profile, the saturated flux shows a quadratic increase with the strength of the flow, and for parabolic profile, a cubic increase. The velocity distribution functions are used to interpret the results.

In this work the 4-(trans-$4^{\prime }\text{−}n$-hexylcyclohexyl)-isothiocyanatobenzene (6CHBT) liquid crystal was doped with differently shaped magnetite nanoparticles. The structural changes were observed by capacitance measurements and showed significant influence of the shape and size of the magnetic particles on the magnetic Fréedericksz transition. For the volume concentration $\varphi =2\times {10}^{-4}$ of the magnetic particles, the critical magnetic field was established for the pure liquid crystal, and for liquid crystals doped with spherical, chainlike, and rodlike magnetic particles. The influence of the magnetic field depends on the type of anchoring, which is characterized by the density of anchoring energy and by the initial orientation between the liquid crystal molecules and the magnetic moment of the magnetic particles. The experimental results indicated soft anchoring in the case of spherical magnetic particles and rigid anchoring in the case of rodlike and chainlike magnetic particles, with parallel initial orientation between the magnetic moments of the magnetic particles and director.

Experimentally it is possible to manipulate the director in a (chiral) smectic-$A$ elastomer using an electric field. This suggests that the director is not necessarily locked to the layer normal, as described in earlier papers that extended rubber elasticity theory to smectics. Here, we consider the case that the director is weakly anchored to the layer normal assuming that there is a free energy penalty associated with relative tilt between the two. We use a recently developed weak-anchoring generalization of rubber elastic approaches to smectic elastomers and study shearing in the plane of the layers, stretching in the plane of the layers, and compression and elongation parallel to the layer normal. We calculate, inter alia, the engineering stress and the tilt angle between director and layer normal as functions of the applied deformation. For the latter three deformations, our results predict the existence of an instability towards the development of shear accompanied by smectic-$C$-like order.

We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our analytical formulas are tested with numerical Monte Carlo simulations.