We study the impact of network heterogeneity on relaxation dynamics of the Kuramoto model on uncorrelated complex networks with scale-free degree distributions. Using the Ott-Antonsen method and the annealed-network approach, we find that the critical behavior of the relaxation rate near the synchronization phase transition does not depend on network heterogeneity and critical slowing down takes place at the critical point when the second moment of the degree distribution is finite. In the case of a complete graph we obtain an explicit result for the relaxation rate when the distribution of natural frequencies is Lorentzian. We also find a response of the Kuramoto model to an external field and show that the susceptibility of the model is inversely proportional to the relaxation rate. We reveal that network heterogeneity strongly impacts a field dependence of the relaxation rate and the susceptibility when the network has a divergent fourth moment of degree distribution. We introduce a pair correlation function of phase oscillators and show that it has a sharp peak at the critical point, signaling emergence of long-range correlations. Our numerical simulations of the Kuramoto model support our analytical results.

We study instabilities and relaxation to equilibrium in a long-range extension of the Fermi-Pasta-Ulam-Tsingou (FPU) oscillator chain by exciting initially the lowest Fourier mode. Localization in mode space is stronger for the long-range FPU model. This allows us to uncover the sporadic nature of instabilities, i.e., by varying initially the excitation amplitude of the lowest mode, which is the control parameter, instabilities occur in narrow amplitude intervals. Only for sufficiently large values of the amplitude, the system enters a permanently unstable regime. These findings also clarify the long-standing problem of the relaxation to equilibrium in the short-range FPU model. Because of the weaker localization in mode space of this latter model, the transfer of energy is retarded and relaxation occurs on a much longer timescale.

We analyze the quintic integrable equation of the nonlinear Schrödinger hierarchy that includes fifth-order dispersion with matching higher-order nonlinear terms. We show that a breather solution of this equation can be converted into a nonpulsating soliton solution on a background. We calculate the locus of the eigenvalues on the complex plane which convert breathers into solitons. This transformation does not have an analog in the standard nonlinear Schrödinger equation. We also study the interaction between the new type of solitons, as well as between breathers and these solitons.

Aligned superhydrophobic surfaces with the same texture orientation reduce drag in the channel and generate secondary flows transverse to the direction of the applied pressure gradient. Here we show that a transverse shear can be easily generated by using superhydrophobic channels with misaligned textured surfaces. We propose a general theoretical approach to quantify this transverse flow by introducing the concept of an effective shear tensor. To illustrate its use, we present approximate theoretical solutions and Dissipative Particle Dynamics simulations for striped superhydrophobic channels. Our results demonstrate that the transverse shear leads to complex flow patterns, which provide a new mechanism of a passive vertical mixing at the scale of a texture period. Depending on the value of Reynolds number two different scenarios occur. At relatively low Reynolds number the flow represents a transverse shear superimposed with two corotating vortices. For larger Reynolds number these vortices become isolated, by suppressing fluid transport in the transverse direction.

It is shown that the universally unstable kinetic drift wave in an electron-ion plasma can very effectively be suppressed by adding an extra flowing ion (or plasma) population. The effect of the flow of the added ions is essential, their response is of the type $(v_{ph}-v_{f0})exp[-{(v_{ph}-v_{f0})}^2]$, where $v_{f0}$ is the flow speed and $v_{ph}$ is the phase speed parallel to the magnetic field vector. The damping is strong and it is mainly due to this ion exponential term, and this remains so for $v_{f0}<v_{ph}$.

We conducted molecular dynamics simulations combined with distance-based umbrella sampling and forward flux sampling to investigate the early stages of protein crystallization. Formation of contacts with long-range interactions and/or an exposed position on the protein surface was kinetically preferred over more stable hydrophobic contacts with a shorter attractive range, while the thermodynamic stability of the protein crystal was provided by hydrophobic interactions. Contacts with a large interaction area showed complex dissociation pathways that were not detected by distance-based umbrella sampling. Instead, forward flux sampling simulations of contact dissociation identified long-range attractive interactions.

A new pairwise Nosé-Hoover type thermostat for molecular dynamics (MD) simulations which is similar in construction to the pair-velocity thermostat of Allen and Schmid, [Mol. Simul. 33, 21 (2007)] (AS) but is based on the configurational thermostat is proposed and tested. Both thermostats generate the canonical velocity distribution, are Galilean invariant, and conserve linear and angular momentum. The unique feature of the pairwise thermostats is an unconditional conservation of the total angular momentum, which is important for thermalizing isolated systems and those nonequilibrium bulk systems manifesting local rotating currents. These thermostats were benchmarked against the corresponding Nosé-Hoover (NH) and Braga-Travis prescriptions, being based on the kinetic and configurational definitions of temperature, respectively. Some differences between the shear-rate-dependent shear viscosity from Sllod nonequilibrium MD are observed at high shear rates using the different thermostats. The thermostats based on the configurational temperature produced very similar monotically decaying shear viscosity (shear thinning) with increasing shear rate, while the NH method showed discontinuous shear thinning into a string phase, and the AS method produced a continuous increase of viscosity (shear thickening), after a shear thinning region at lower shear rates. Both pairwise additive thermostats are neither purely kinetic nor configurational in definition, and possible directions for further improvement in certain aspects are discussed.

Surface nanobubbles are experimentally known to survive for days at hydrophobic surfaces immersed in gas-oversaturated water. This is different from bulk nanobubbles, which are pressed out by the Laplace pressure against any gas oversaturation and dissolve in submilliseconds, as derived by Epstein and Plesset [J. Chem. Phys. 18, 1505 (1950)]. Pinning of the contact line has been speculated to be the reason for the stability of the surface nanobubbles. Building on an exact result by Popov [Phys. Rev. E 71, 036313 (2005)] on coffee stain evaporation, here we confirm this speculation by an exact calculation for single surface nanobubbles. It is based only on (i) the diffusion equation, (ii) Laplace pressure, and (iii) Henry's equation, i.e., fluid dynamical equations which are all known to be valid down to the nanometer scale. The crucial parameter is the gas oversaturation $\zeta$ of the liquid. At the stable equilibrium, the gas overpressures due to this oversaturation and the Laplace pressure balance. The theory predicts how the contact angle of the pinned bubble depends on $\zeta$ and the surface nanobubble's footprint lateral extension $L$. It also predicts an upper lateral extension threshold for stable surface nanobubbles to exist.

We investigate the simple one-dimensional driven model, the totally asymmetric exclusion process, coupled to mutually interactive Langmuir kinetics. This model is motivated by recent studies on clustering of motor proteins on microtubules. In the proposed model, the attachment and detachment rates of a particle are modified depending upon the occupancy of neighboring sites. We first obtain continuum mean-field equations and in certain limiting cases obtain analytic solutions. We show how mutual interactions increase (decrease) the effects of boundaries on the phase behavior of the model. We perform Monte Carlo simulations and demonstrate that our analytical approximations are in good agreement with the numerics over a wide range of model parameters. We present phase diagrams over a selective range of parameters.

In the Hamiltonian mean-field model, we study the core-halo structure of low-energy quasistationary states under unsteady water-bag type initial conditions. The core-halo structure results in the superposition of two independent Lynden-Bell distributions. We examine the completeness of the Lynden-Bell relaxation and the relaxation between these two Lynden-Bell distributions.

The phase transitions occurring in the frustrated Ising square antiferromagnet with first- $\left(J_1<0\right)$ and second-nearest-neighbor $\left(J_2<0\right)$ interactions are studied within the framework of the effective-field theory with correlations based on the different cluster sizes and for a wide range of $R=J_2/\left|J_1\right|$. Despite the simplicity of the model, it has proved difficult to precisely determine the order of the phase transitions. In contrast to the previous effective-field study, we have found a first-order transition line in the region close to $R=-0.5$ not only between the superantiferromagnetic and paramagnetic $\left(R<-0.5\right)$ but also between antiferromagnetic and paramagnetic $\left(R>-0.5\right)$ phases.

The bicritical properties of the three-dimensional classical anisotropic Heisenberg model in a crystal field are investigated through extensive Monte Carlo simulations on a simple cubic lattice, using Metropolis and Wolff algorithms. Field-mixing and multidimensional histogram techniques were employed in order to compute the probability distribution function of the extensive conjugate variables of interest and, using finite-size scaling analysis, the first-order transition line of the model was precisely located. The fourth-order cumulant of the order parameter was then calculated along this line and the bicritical point located with good precision from the cumulant crossings. The bicritical properties of this point were further investigated through the measurement of the universal probability distribution function of the order parameter. The results lead us to conclude that the studied bicritical point belongs in fact to the three-dimensional Heisenberg universality class.

The behaviors of granular systems are sensitive to a wide variety of particle properties, including size, density, elasticity, and shape. Differences in any of these properties between particles in a granular mixture may lead to segregation, or “demixing,” a process of great industrial relevance. Despite the known influence of particle geometry in granular systems, a considerable fraction of research into these systems concerns only uniformly spherical particles. We address, for the case of vertically vibrated granular systems, the important question of whether the introduction of differing particle geometries entirely invalidates our existing knowledge based on purely spherical granulates, or whether current models may simply be adapted to account for the effects of particle shape. We demonstrate that while shape effects can indeed influence the dynamical and segregative behaviors of a granular system, the segregative mechanisms associated with particle geometry are decidedly secondary to those related to particle density. The relevant control parameters determining the extent of geometrically induced segregation are established. Finally, a manner in which shape effects may be accounted for in simulations utilizing purely spherical particles is proposed.

We investigate the onset of wall-induced convection in vertically vibrated granular matter by means of experiments and two-dimensional computer simulations. In both simulations and experiments we find that the wall-induced convection occurs inside the bouncing bed region of the parameter space, in which the granular bed behaves like a bouncing ball. A good agreement between experiments and simulations is found for the peak vibration acceleration at which convection starts. By comparing the results of simulations initialized with and without defects, we find that the onset of convection occurs at lower vibration strengths in the presence of defects. Furthermore, we find that the convection of granular particles initialized in a perfect hexagonal lattice is related to the nucleation of defects and the process is described by an Arrhenius law.

We construct an individual-based metapopulation model of population genetics featuring migration, mutation, selection, and genetic drift. In the case of a single “island,” the model reduces to the Moran model. Using the diffusion approximation and time-scale separation arguments, an effective one-variable description of the model is developed. The effective description bears similarities to the well-mixed Moran model with effective parameters that depend on the network structure and island sizes, and it is amenable to analysis. Predictions from the reduced theory match the results from stochastic simulations across a range of parameters. The nature of the fast-variable elimination technique we adopt is further studied by applying it to a linear system, where it provides a precise description of the slow dynamics in the limit of large time-scale separation.

One of the defining characteristics of turbulence is its ability to promote mixing. We present here a case where the opposite happens—simulation results indicate that particles can separate near the wall of a turbulent channel flow, when they have sufficiently different Schmidt numbers without use of any other means. The physical mechanism of the separation is understood when the interplay between convection and diffusion, as expressed by their characteristic time scales, is considered, leading to the determination of the necessary conditions for a successful separation between particles. Practical applications of these results can be found when very small particles need to be separated or removed from a fluid.

A 263-nm Thomson-scattering beam was used to directly probe two-plasmon-decay (TPD) excited electron plasma waves (EPWs) driven by between two and five 351-nm beams on the OMEGA Laser System. The amplitude of these waves was nearly independent of the number of drive beams at constant overlapped intensity, showing that the observed EPWs are common to the multiple beams. In an experimental configuration where the Thomson-scattering diagnostic was not wave matched to the common TPD EPWs, a broad spectrum of TPD-driven EPWs was observed, indicative of nonlinear effects associated with TPD saturation. Electron plasma waves corresponding to Langmuir decay of TPD EPWs were observed in both Thomson-scattering spectra, suggesting the Langmuir decay instability as a TPD saturation mechanism. Simulated Thomson-scattering spectra from three-dimensional numerical solutions of the extended Zakharov equations of TPD are in excellent agreement with the experimental spectra and verify the presence of the Langmuir decay instability.

The thermodynamic curvature scalar $R$ is evaluated for supercooled water with a two-state equation of state correlated with the most recent available experimental data. This model assumes a liquid-liquid critical point. Our investigation extends the understanding of the thermodynamic behavior of $R$ considerably. We show that $R$ diverges to $-\infty$ when approaching the assumed liquid-liquid critical point. This limit is consistent with all of the fluid critical point models known so far. In addition, we demonstrate a sign change of $R$ along the liquid-liquid line from negative near the critical point to positive on moving away from the critical point in the low density “ice-like” liquid phase. We also trace out the Widom line in phase space. In addition, we investigate increasing correlation length in supercooled water and compare our results with recent published small angle x-ray scattering measurements.

We study the evolution of spin clusters on two-dimensional slices of the three-dimensional Ising model in contact with a heat bath after a sudden quench to a subcritical temperature. We analyze the evolution of some simple initial configurations, such as a sphere and a torus, of one phase embedded into the other, to confirm that their area disappears linearly with time and to establish the temperature dependence of the prefactor in each case. Two generic kinds of initial states are later used: equilibrium configurations either at infinite temperature or at the paramagnetic-ferromagnetic phase transition. We investigate the morphological domain structure of the coarsening configurations on two-dimensional slices of the three-dimensional system, compared with the behavior of the bidimensional model.

We study the organization of finite-size, large ensembles of phase oscillators networking via scale-free topologies in the presence of a positive correlation between the oscillators' natural frequencies and the network's degrees. Under those circumstances, abrupt transitions to synchronization are known to occur in growing scale-free networks, while the transition has a completely different nature for static random configurations preserving the same structure-dynamics correlation. We show that the further presence of degree-degree correlations in the network structure has important consequences on the nature of the phase transition characterizing the passage from the phase-incoherent to the phase-coherent network state. While high levels of positive and negative mixing consistently induce a second-order phase transition, moderate values of assortative mixing, such as those ubiquitously characterizing social networks in the real world, greatly enhance the irreversible nature of explosive synchronization in scale-free networks. The latter effect corresponds to a maximization of the area and of the width of the hysteretic loop that differentiates the forward and backward transitions to synchronization.