We developed a scheme for evaluating the size of the largest connected subnetwork (giant component) in random networks and the percolation threshold when sites (nodes) and/or bonds (edges) are removed from the networks based on the cavity method of statistical mechanics of disordered systems. We apply our scheme particularly to random networks of bimodal degree distribution (two-peak networks), which have been proposed in earlier studies as robust networks against random failures of site and/or targeted (random degree-dependent) attacks on sites. Our analysis indicates that the correlations among degrees affect a network’s robustness against targeted attacks on sites or bonds nontrivially depending on details of network configurations.

We show that the load at each node in a preferential attachment network scales as a power of the degree of the node. For a network whose degree distribution is $p\left(k\right)\sim k^{-\gamma }$, we show that the load is $l\left(k\right)\sim k^{\eta }$ with $\eta =\gamma -1$, implying that the probability distribution for the load is $p\left(l\right)\sim 1/l^2$ independent of $\gamma$. The results are obtained through scaling arguments supported by finite size scaling studies. They contradict earlier claims, but are in agreement with the exact solution for the special case of tree graphs. Results are also presented for real communications networks at the IP layer, using the latest available data. Our analysis of the data shows relatively poor power-law degree distributions as compared to the scaling of the load versus degree. This emphasizes the importance of the load in network analysis.

We study synchronization in the two-dimensional lattice of coupled phase oscillators with random intrinsic frequencies. When the coupling $K$ is larger than a threshold $K_E$, there is a macroscopic cluster of frequency-synchronized oscillators. We explain why the macroscopic cluster disappears at $K_E$. We view the system in terms of vortices, since cluster boundaries are delineated by the motion of these topological defects. In the entrained phase $\left(K>K_E\right)$, vortices move in fixed paths around clusters, while in the unentrained phase $\left(K<K_E\right)$, vortices sometimes wander off. These deviant vortices are responsible for the disappearance of the macroscopic cluster. The regularity of vortex motion is determined by whether clusters behave as single effective oscillators. The unentrained phase is also characterized by time-dependent cluster structure and the presence of chaos. Thus, the entrainment transition is actually an order-chaos transition. We present an analytical argument for the scaling $K_E\sim K_L$ for small lattices, where $K_L$ is the threshold for phase locking. By also deriving the scaling $K_L\sim \text{log}N$, we thus show that $K_E\sim \text{log}N$ for small $N$, in agreement with numerics. In addition, we show how to use the linearized model to predict where vortices are generated.

After impact onto a smooth dry surface, a drop of viscous liquid initially spreads in the form of a thick lamella. If the drop splashes, it first emits a thin fluid sheet that can ultimately break up into droplets causing the splash. Ambient gas is crucial for creating this thin sheet. The time for sheet ejection, $t_{ejt}$, depends on impact velocity, liquid viscosity, gas pressure, and molecular weight. A central air bubble is trapped below the drop at pressures even below that necessary for this sheet formation. In addition, air bubbles are entrained underneath the spreading lamella when the ejected sheet is present. Air entrainment ceases at a lamella velocity that is independent of drop impact velocity as well as ambient gas pressure.

Drying experiments have been carried out with model soils made of different pastes filling granular packings. A detailed information concerning the time evolution of the water saturation distribution inside the sample was obtained from magnetic resonance imaging measurements. This study makes it possible to understand the physical origin of the drying characteristics of these materials. The drying curves exhibit a constant-rate period (CRP) and a falling-rate period (FRP) but the relative durations of these periods depend on the paste structure. With a kaolin suspension the CRP lasts down to very low water densities and is associated with a homogeneous drying of the paste throughout the sample. With a bentonite suspension the CRP is shorter and the drying in the FRP results from a complex process involving fractures progressing downward through the pasty matrix. With a gel the CRP period is even shorter and the drying in the FRP results from the progression of a dry front through the packing as a result of the shrinkage of the gel matrix. This provides an overview of the main possible processes at work when drying a soil as a function of its components along with some practical means for slowing down drying from soils.

We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed global feedback). We explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a Hopf bifurcation as the delay time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.

The formation of small but finite amplitude electrostatic shocks in the propagation of quantum ion-acoustic waves obliquely to an external magnetic field is reported in a quantum electron-positron-ion plasma. Such shocks are seen to have double-layer (DL) structures composed of the compressive and accompanying rarefactive slow-wave fronts. Existence of such DL shocks depends critically on the quantum coupling parameter $H$ associated with the Bohm potential and the positron to electron density ratio $\delta$. The profiles may, however, steepen initially and reach a steady state with a number of solitary waves in front of the shocks. Such novel DL shocks could be a good candidate for particle acceleration in intense laser-solid density plasma interaction experiments as well as in compact astrophysical objects, e.g., magnetized white dwarfs.

The rectification of a single file of attracting particles subjected to a low frequency ac drive is proposed as a working mechanism for particle shuttling in an asymmetric narrow channel. Increasing the particle attraction results in the file condensing, as signaled by the dramatic enhancement of the net particle current. The magnitude and direction of the current become extremely sensitive to the actual size of the condensate, which can then be made to shuttle between two docking stations, transporting particles in one direction, with an efficiency much larger than conventional diffusive models predict.

We study the bursting dynamics of a thin oil film sandwiched by glycerol aqueous solution in a confined geometry where the circular symmetry of the bursting hole is broken. We find that the bursting proceeds with a constant velocity except for initial times and the velocity is governed by the viscosity of the surrounding glycerol. Different from previous studies where the bursting speed is constant, in our confined geometry no rims are formed at the bursting tip as a result of the symmetry breaking. Our findings can be explained by original and simple scaling arguments.

Stochastic dynamics in the energy representation is used as a method to represent nonequilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin equation with multiplicative noise. Properties of the steady states are examined by solving the Fokker-Planck equation for the energy distribution functions. The generalized integral fluctuation theorem is deduced for the systems characterized by the shifted probability flux operator. From this theorem, a number of entropy and fluctuation relations such as the Evans-Searles fluctuation theorem, the Hatano-Sasa identity, and the Jarzynski’s equality are derived.

The $q$-state clock model with the cosine potential has a single phase transition for $q\le 4$ and two transitions for $q\ge 5$. It is shown by Monte Carlo simulations that the helicity modulus for the five-state clock model $\left(q=5\right)$ does not vanish at the high-temperature transition. This is in contrast to the clock models with $q\ge 6$ for which the helicity modulus vanishes. This means that the transition for the five-state clock model differs from the Kosterlitz-Thouless (KT) transition. It is also shown that this change in the transition is caused by an interplay between the number of angular directions and the interaction potential: by slightly modifying the interaction potential, the KT transition for $q=6$ turns into the same non-KT transition. Likewise, the KT transition is recovered for $q=5$ when the Villain potential is used. Comparisons with other clock-model results are made and discussed.

We have investigated a polymer growth process on the triangular lattice where the configurations produced are self-avoiding trails. We show that the scaling behavior of this process is similar to the analogous process on the square lattice. However, while the square lattice process maps to the collapse transition of the canonical interacting self-avoiding trail (ISAT) model on that lattice, the process on the triangular lattice model does not map to the canonical equilibrium model. On the other hand, we show that the collapse transition of the canonical ISAT model on the triangular lattice behaves in a way reminiscent of the $\theta$ point of the interacting self-avoiding walk (ISAW) model, which is the standard model of polymer collapse. This implies an unusual lattice dependency of the ISAT collapse transition in two dimensions. By studying an extended ISAT model, we demonstrate that the growth process maps to a multicritical point in a larger parameter space. In this extended parameter space the collapse phase transition may be either $\theta$-point-like (second order) or first order, and these two are separated by a multicritical point. It is this multicritical point to which the growth process maps. Furthermore, we provide evidence that in addition to the high-temperature gaslike swollen polymer phase (coil) and the low-temperature liquid-drop-like collapse phase (globule) there is also a maximally dense crystal-like phase (crystal) at low temperatures dependent on the parameter values. The multicritical point is the meeting point of these three phases. Our hypothesized phase diagram resolves the mystery of the seemingly differing behaviors of the ISAW and ISAT models in two dimensions as well as the behavior of the trail growth process.

Two important enhanced sampling algorithms, simulated (ST) and parallel (PT) tempering, are commonly used when ergodic simulations may be hard to achieve, e.g., due to a phase space separated by large free-energy barriers. This is so for systems around first-order phase transitions, a case still not fully explored with such approaches in the literature. In this contribution we make a comparative study between the PT and ST for the Ising (a lattice gas in the fluid language) and the Blume–Emery–Griffiths (a lattice gas with vacancies) models at phase-transition regimes. We show that although the two methods are equivalent in the limit of sufficiently long simulations, the PT is more advantageous than the ST with respect to all the analysis performed: convergence toward the stationarity; frequency of tunneling between phases at the coexistence; and decay of time-displaced correlation functions of thermodynamic quantities. Qualitative arguments for why one may expect better results from the PT than the ST near phase-transitions conditions are also presented.

The problem of Laplacian growth in two dimensions is considered within the Loewner-equation framework. Initially the problem of fingered growth is revisited and an exact solution for a three-finger configuration is reported. Then a general class of growth models for an interface growing in the upper half-plane is introduced and the corresponding Loewner equation for the problem is derived. Several examples are given including interfaces with one or more tips as well as multiple growing interfaces. A generalization of our interface growth model in terms of “Loewner domains,” where the growth rule is specified by a time evolving measure, is briefly discussed.

In this paper we present a direct measurement of stretched chain conformation in polymer nanocomposites in a large range of deformation using a specific contrast-matched small angle neutron scatttering (SANS) method. Whatever are the filler structure and the chain length the results show a clear identity of chain deformation in pure and reinforced polymer and offer more insight on the polymer chain contribution in the mechanical reinforcement. It suggests that glassy layer or glassy paths, recently proposed, should involve only a small fraction of chains. As a result, the remaining filler contribution appears strikingly constant with deformation as explained by continuous locking-unlocking rearrangement process of the particles.

We experimentally study synchronization processes in a system of two different multisection semiconductor lasers. Periodic self-pulsations of laser 1 are injected into laser 2, which is operating in a regime with two-frequency quasiperiodic self-pulsations. The experimental system demonstrates the new type of transitions to synchrony between three frequencies which has been recently revealed using generic coupled phase and van der Pol oscillator models. In particular, resonances of quasiperiodic oscillations at integer winding numbers three and five are shown to break up before locking to the injected periodic signal. Moreover, carefully determining the coherence of the noisy oscillations, we reveal so far unexplored processes of coherence transfer to nonsynchronized oscillations.

Heterogeneity in the degree distribution is known to suppress global synchronization in complex networks of symmetrically coupled oscillators. Scale-free networks display a great deal of heterogeneity, containing a few nodes, termed hubs, that are highly connected, while most nodes receive only a few connections. Here, we show that a group of synchronized nodes may appear in scale-free networks: hubs undergo a transition to synchronization while the other nodes remain unsynchronized. This general phenomenon can occur even in the absence of global synchronization. Our results suggest that scale-free networks may have evolved to complement various levels of synchronization.

The Bödewadt boundary layer flow on the stationary bottom end wall of a finite rotating cylinder is very sensitive to perturbations and noise. Axisymmetric radial waves propagating inward have been observed experimentally and numerically before the appearance of spiral three-dimensional instabilities. In this study, the sensitivity and response of the finite Bödewadt flow to a harmonic modulation of the rotation rate are analyzed. A comprehensive exploration of response to variations in the amplitude and frequency of the forcing has been carried out. There are sharply delineated linear- and nonlinear-response regimes, with a sharp transition between them at moderate amplitudes. The periodic forcing leads to a steady-streaming flow, even in the linear-response regime, and to a period-doubling bifurcation in the nonlinear regime. Frequency response curves at different forcing amplitudes over a wide range of frequencies have been computed and used to identify the frequency band that excites the axisymmetric radial waves and the forcing frequency that elicits the strongest response. Finally, we have shown that the axisymmetric waves always decay to the steady basic state when the harmonic modulation is suppressed, and conclude that the experimentally observed persistent circular waves are not self-sustained.

A simple minimally perturbative method is introduced which provides the ability to experimentally measure both the radial confining potential and the interaction potential between two individual dust particles, levitated in the sheath of a radio-frequency (RF) argon discharge. In this technique, a single dust particle is dropped into the plasma sheath to interact with a second individual dust particle already situated at the system’s equilibrium point, without introducing any external perturbation. The resulting data are analyzed using a method employing a polynomial fit to the particle displacement(s), $X\left(t\right)$, to reduce uncertainty in calculation. Employing this technique, the horizontal confinement is shown to be parabolic over a wide range of pressures and displacements from the equilibrium point. The interaction potential is also measured and shown to be well described by a screened Coulomb potential and to decrease with increasing pressure. Finally, the charge on the particle and the effective dust screening distance are calculated. It is shown for the first time experimentally that the charge on a particle in the sheath of an RF plasma decreases with increasing pressure, in agreement with theoretical predictions. The screening distance also decreases with increasing pressure as expected. This technique can be used for rapid determination of particle parameters in dusty plasma.

We study a nanoscale system composed of one corrugated cylinder (pinion) and one corrugated plate (rack). The pinion and rack have no mechanical contact, but are coupled via the lateral Casimir force. We consider the case where the rack position versus time is a periodic triangular signal. We find that the device can rectify the periodic but nonsinusoidal motion of the rack. Using the typical values of parameters, we find that the pinion rotates with an average angular velocity $\Omega =1\sim 100\text{Hz}$. Experimental observation of the pinion rotation will show that the quantum vacuum can intermesh the noncontact parts of nanomachines.