In this article, we investigate the dynamical behavior of breathers in optoelectronic oscillators from the standpoint of mixed-mode oscillations. In the phase space, these breathers are composite oscillations that are damped to the attractive branches of an invariant manifold. Our study shows that the emergence of breather dynamics is linked to the apparition of inflection points in the phase space, and we develop an analytical framework based on the Liénard reduction form in order to provide an analytical insight into this phenomenology. Our theoretical results are in excellent agreement with experimental measurements.

An important environmental application of pattern control by periodic spatial forcing is the restoration of vegetation patterns in water-limited ecosystems that went through desertification. Vegetation restoration is often based on periodic landscape modulations that intercept overland water flow and form favorable conditions for vegetation growth. Viewing this method as a spatial resonance problem, we show that plain realizations of this method, assuming a complete vegetation response to the imposed modulation pattern, suffer from poor resilience to rainfall variability. By contrast, less intuitive realizations, based on the inherent spatial modes of vegetation growth and involving partial vegetation implantation, can be highly resilient and equally productive. We derive these results using two complementary models, a realistic vegetation model, and a simple pattern formation model that lends itself to mathematical analysis and highlights the universal aspects of the behaviors found with the vegetation model. We focus on reversing desertification as an outstanding environmental problem, but the main conclusions hold for any spatially forced system near the onset of a finite-wave-number instability that is subjected to noisy conditions.

We explore ensemble inequivalence in long-range interacting systems by studying an $XY$ model of classical spins with ferromagnetic and nematic coupling. We demonstrate the inequivalence by mapping the microcanonical phase diagram onto the canonical one, and also by doing the inverse mapping. We show that the equilibrium phase diagrams within the two ensembles strongly disagree within the regions of first-order transitions, exhibiting interesting features like temperature jumps. In particular, we discuss the coexistence and forbidden regions of different macroscopic states in both the phase diagrams.

Making use of the classical second-moment sum rule, it is possible to convert a series of constant-$Q$ x-ray Brillouin scattering scans ($Q$ momentum transfer) into a series of constant frequency scans over the measured $Q$ range. The method is applied to literature results for the longitudinal phonon dispersion in several glass formers. The constant frequency scans are well fitted in terms of a $Q$-independent phonon damping depending exclusively on the frequency, in agreement with two recent theories of the boson peak. The method allows us to link the x-ray Brillouin scattering to the diffuse Umklapp scattering from the boson peak vibrations at higher momentum transfer on an absolute intensity scale.

We investigate hitherto-unexplored flow characteristics inside a sessile droplet evaporating on heated hydrophobic and superhydrophobic surfaces and propose the use of evaporation-induced flow as a means to promote efficient “on-the-spot” mixing in microliter-sized droplets. Evaporative cooling at the droplet interface establishes a temperature gradient that induces buoyancy-driven convection inside the droplet. An asymmetric single-roll flow pattern is observed on the superhydrophobic substrate, in stark contrast with the axisymmetric toroidal flow pattern that develops on the hydrophobic substrate. The difference in flow patterns is attributed to the larger height-to-diameter aspect ratio of the droplet (of the same volume) on the superhydrophobic substrate, which dictates a single asymmetric vortex as the stable buoyancy-induced convection mode. A scaling analysis relates the observed velocities inside the droplet to the Rayleigh number. On account of the difference in flow patterns, Rayleigh numbers, and the reduced solid-liquid contact area, the flow velocity is an order of magnitude higher in droplets evaporating on a superhydrophobic substrate as compared to hydrophobic substrates. Flow velocities in all cases are shown to increase with substrate temperature and droplet size: The characteristic time required for mixing of a dye in an evaporating sessile droplet is reduced by ∼8 times on a superhydrophobic surface when the substrate temperature is increased from 40 to 60 °C. The mixing rate is ∼15 times faster on the superhydrophobic substrate compared to the hydrophobic surface maintained at the same temperature of 60 °C.

Multiplex networks describe a large number of systems ranging from social networks to the brain. These multilayer structure encode information in their structure. This information can be extracted by measuring the correlations present in the multiplex networks structure, such as the overlap of the links in different layers. Many multiplex networks are also weighted, and the weights of the links can be strongly correlated with the structural properties of the multiplex network. For example, in multiplex network formed by the citation and collaboration networks between PRE scientists it was found that the statistical properties of citations to coauthors differ from the one of citations to noncoauthors, i.e., the weights depend on the overlap of the links. Here we present a theoretical framework for modeling multiplex weighted networks with different types of correlations between weights and overlap. To this end, we use the framework of canonical network ensembles, and the recently introduced concept of multilinks, showing that null models of a large variety of network structures can be constructed in this way. In order to provide a concrete example of how this framework apply to real data we consider a multiplex constructed from gene expression data of healthy and cancer tissues.

The phase space of a typical Hamiltonian system contains both chaotic and regular orbits, mixed in a complex, fractal pattern. One oft-studied phenomenon is the algebraic decay of correlations and recurrence time distributions. For area-preserving maps, this has been attributed to the stickiness of boundary circles, which separate chaotic and regular components. Though such dynamics has been extensively studied, a full understanding depends on many fine details that typically are beyond experimental and numerical resolution. This calls for a statistical approach, the subject of the present work. We calculate the statistics of the boundary circle winding numbers, contrasting the distribution of the elements of their continued fractions to that for uniformly selected irrationals. Since phase space transport is of great interest for dynamics, we compute the distributions of fluxes through island chains. Analytical fits show that the “level” and “class” distributions are distinct, and evidence for their universality is given.

We systematically investigate the spontaneous packaging mechanism of a single polyelectrolyte chain into an oppositely charged nanocavity by Langevin molecular dynamics simulations of a generic coarse-grained model. Intrusion dynamics and packaging rate, as well as the self-assembly process inside turn out to depend sensitively on the stiffness of the polyelectrolyte, the surface charge density inside the capsid, and the radius of the cavity. Further analysis shows that, depending on the stiffness, thermal fluctuations and charge inversion can be important factors to overcome barriers that slow down the intrusion and packaging dynamics. These results help advance our understanding of the function of charges on the inner surface of viral capsids and the possibility to design capsids as synthetic nanocarriers.

We consider the impact of the effective gravitational acceleration on microstructural properties of granular packings through experimental studies of spherical granular materials saturated within fluids of varying density. We characterize the local organization of spheres in terms of contact connectivity, distribution of the Delaunay free volumes, and the shape factor (parameter of nonsphericity) of the Voronoï polygons. The shape factor gives a clear physical picture of the competition between less and more ordered domains of particles in experimentally obtained packings. As the effective gravity increases, the probability distribution of the shape factor becomes narrower and more localized around the lowest values of the shape factor corresponding to regular hexagon. It is found that curves of the pore distributions are asymmetric with a long tail on the right-hand side, which progressively reduces while the effective gravity gets stronger for lower densities of interstitial fluid. We show that the distribution of local areas (Voronoï cells) broadens with decreasing value of the effective gravity due to the formation of lose structures such as large pores and chainlike structures (arches or bridges). Our results should be particularly helpful in testing the newly developed simulation techniques involving liquid-related forces associated with immersed granular particles.

Using Monte Carlo simulations, we study the hysteresis in the unzipping of double-stranded DNA whose ends are subjected to a time-dependent periodic force with frequency ($\omega$) and amplitude ($G$). For the static force, i.e., $\omega \to 0$, the DNA is in equilibrium with no hysteresis. On increasing $\omega$, the area of the hysteresis loop initially increases and becomes maximum at frequency ${\omega }^{*}\left(G\right)$, which depends on the force amplitude $G$. If the frequency is increased further, we find that for lower amplitudes the loop area decreases monotonically to zero, but for higher amplitudes it has an oscillatory component. The height of subsequent peaks decreases, and finally the loop area becomes zero at very high frequencies. The number of peaks depends on the length of the DNA. We give a simple analysis to estimate the frequencies at which maxima and minima occur in the loop area. We find that the area of the hysteresis loop scales as $1/\omega$ in the high-frequency regime, whereas it scales as $G^{\alpha }{\omega }^{\beta }$ with exponents $\alpha =1$ and $\beta =5/4$ at low frequencies. The values of the exponents $\alpha$ and $\beta$ are different from the exponents reported earlier based on the hysteresis of small hairpins.

We present a unified view of finite-size scaling (FSS) in dimension $d$ above the upper critical dimension, for both free and periodic boundary conditions. We find that the modified FSS proposed some time ago to allow for violation of hyperscaling due to a dangerous irrelevant variable applies only to $\mathbf{k}=\mathbf{0}$ fluctuations, and “standard” FSS applies to $\mathbf{k}\ne \mathbf{0}$ fluctuations. Hence the exponent $\eta$ describing power-law decay of correlations at criticality is unambiguously $\eta =0$. With free boundary conditions, the finite-size “shift” is greater than the rounding. Nonetheless, using $T-T_L$, where $T_L$ is the finite-size pseudocritical temperature, rather than $T-T_c$, as the scaling variable, the data do collapse onto a scaling form that includes the behavior both at $T_L$, where the susceptibility $\chi$ diverges like $L^{d/2}$, and at the bulk $T_c$, where it diverges like $L^2$. These claims are supported by large-scale simulations on the five-dimensional Ising model.

For a random walk on a confined one-dimensional domain, we consider mean first-passage times (MFPT) in the presence of a mobile trap. The question we address is whether a mobile trap can improve capture times over a stationary trap. We consider two scenarios: a randomly moving trap and an oscillating trap. In both cases, we find that a stationary trap actually performs better (in terms of reducing expected capture time) than a very slowly moving trap; however, a trap moving sufficiently fast performs better than a stationary trap. We explicitly compute the thresholds that separate the two regimes. In addition, we find a surprising relation between the oscillating trap problem and a moving-sink problem that describes reduced dynamics of a single spike in a certain regime of the Gray-Scott model. Namely, the above-mentioned threshold corresponds precisely to a Hopf bifurcation that induces oscillatory motion in the location of the spike. We use this correspondence to prove the uniqueness of the Hopf bifurcation.

We construct and analyze a model for a disordered linear spring network with anisotropy. The modeling is motivated by, for example, granular systems, nematic elastomers, and ultimately cytoskeletal networks exhibiting some underlying anisotropy. The model consists of a triangular lattice with two different bond occupation probabilities, $p_x$ and $p_y$, for the linear springs. We develop an effective medium theory (EMT) to describe the network elasticity as a function of $p_x$ and $p_y$. We find that the onset of rigidity in the EMT agrees with Maxwell constraint counting. We also find beyond linear behavior in the shear and bulk modulus as a function of occupation probability in the rigid phase for small strains, which differs from the isotropic case. We compare our EMT with numerical simulations to find rather good agreement. Finally, we discuss the implications of extending the reach of effective medium theory as well as draw connections with prior work on both anisotropic and isotropic spring networks.

A necessary condition to optimize work output is obtained for general heat engines working between two finite-sized heat reservoirs in a given period of time $\tau$, with the amount of heat received from the hot reservoir being fixed for all possible realizations of the process. It states that $T_{\mathrm{c}}\dot{\sigma }$ should be a constant during the optimized process, where $T_{\mathrm{c}}$ is the temperature of the cold reservoir, which could be time dependent, and $\dot{\sigma }$ is the entropy production rate of the two reservoirs. Further optimizing $\tau$ gives the maximum time-averaged power output; the corresponding thermodynamical efficiency, however, is found to be generally not equal to half of the maximum efficiency due to the finiteness of the sizes of two reservoirs. Our results are obtained within the framework of Onsager's theory of linear irreversible thermodynamics and under the tight-coupling condition. The findings in this work may potentially be applied in the optimization of realistic thermodynamical processes.

Three-dimensional molecular-dynamics simulations of cohesive dissipative powders under a plane shear are performed. We find the various phases depending on the dimensionless shear rate and the dissipation rate as well as the density. We also find that the shape of clusters depends on the initial condition of velocities of particles when the dissipation is large. Our simple stochastic model reproduces the non-Gaussian velocity distribution function appearing in the coexistence phase of a gas and a plate.

The article reports the dependence of the conductivity relaxation on temperature T and pressure P in the canonical ionic glass former $0.4\mathrm{Ca}(\mathrm{N}{\mathrm{O}}_3{)}_2\text{−}0.6\mathrm{KN}{\mathrm{O}}_3\left(\mathrm{CKN}\right)$. At constant conductivity relaxation time ${\tau }_{\sigma }$, the entire conductivity relaxation spectra obtained at widely different combinations of T and P superpose almost perfectly, and thus it is the ion-ion interaction but not thermodynamics that determines the frequency dispersion. Moreover, on vitrifying CKN by either elevating P or decreasing T, changes of P or T dependence of ${\tau }_{\sigma }$ at the glass transition pressure $P_g$ and temperature $T_g$ are observed to occur at the same value, i.e., ${\tau }_{\sigma }\left(P_g\right)={\tau }_{\sigma }\left(T_g\right)$, indicating that the relation between ${\tau }_{\sigma }$ and the structural relaxation time ${\tau }_{\alpha }$ is also independent of P and T.

Wertheim's two-density thermodynamic perturbation theory (TPT) has proven to be an indispensable statistical mechanical tool in the description of associating fluids with a single association site. TPT was developed to enforce the monovalence of the hydrogen bond and only recently has been extended to account for divalent association sites. It has been shown through experiment and molecular simulation that certain one-site associating fluids can self-assemble into complex extended supramolecular structures as a result of multiple bonding of association sites. In this paper we reorganize TPT into a form that is more easily applied to complex associated structures. The derived theory is general to all possible self-assemble structures. We obtain the free energy and bonding fractions in a general way in terms of single-cluster partition functions and averages. The new formalism removes any reference to graph theory allowing for the conceptually straightforward application of the two-density formalism to complex self-assembled structures.