The mixing properties of networks are usually inferred by comparing the degree of a node with the average degree of its neighbors. This kind of analysis often leads to incorrect conclusions: Assortative patterns may appear reversed by a mechanism known as Simpson’s paradox. We prove this fact by analytical calculations and simulations on three classes of growing networks based on preferential attachment and fitness, where the disassortative behavior observed is a spurious effect. Our results give a crucial contribution to the debate about the origin of disassortative mixing, since networks previously classified as disassortative reveal instead assortative behavior to a careful analysis.

In the course of certain lung diseases, the surface properties and the amount of fluids coating the airways changes and liquid bridges may form in the small airways blocking the flow of air, impairing gas exchange. During inhalation, these liquid bridges may rupture due to mechanical instability and emit a discrete sound event called pulmonary crackle, which can be heard using a simple stethoscope. We hypothesize that this sound is a result of the acoustical release of energy that had been stored in the surface of liquid bridges prior to its rupture. We develop a lattice gas model capable of describing these phenomena. As a step toward modeling this process, we address a simpler but related problem, that of a liquid bridge between two planar surfaces. This problem has been analytically solved and we use this solution as a validation of the lattice gas model of the liquid bridge rupture. Specifically, we determine the surface free energy and critical stability conditions in a system containing a liquid bridge of volume $\Omega$ formed between two parallel planes, separated by a distance $2h$, with a contact angle $\Theta$ using both Monte Carlo simulation of a lattice gas model and variational calculus based on minimization of the surface area with the volume and the contact angle constraints. In order to simulate systems with different contact angles, we vary the parameters between the constitutive elements of the lattice gas. We numerically and analytically determine the phase diagram of the system as a function of the dimensionless parameters $h{\Omega }^{-1∕3}$ and $\Theta$. The regions of this phase diagram correspond to the mechanical stability and thermodynamical stability of the liquid bridge. We also determine the conditions for the symmetrical versus asymmetrical rupture of the bridge. We numerically and analytically compute the release of free energy during rupture. The simulation results are in agreement with the analytical solution. Furthermore, we discuss the results in connection to the rupture of similar bridges that exist in diseased lungs.

In this paper we present measurements of the secondary electron emission yield $\left(\gamma \right)$ of a carbonaceous dust particle material, which was grown in argon diluted acetylene plasmas. One aim was to reach a better understanding of charging and discharging processes of dust particles in complex plasmas due to secondary electron emission and consequently to try to explain the anomalous behavior of electron density observed in afterglows of pulsed rf plasmas. We compared the results of a simple model and of a Monte Carlo simulation to the previously measured time dependence of the electron density in complex plasma afterglow. It was found that the value of the intrinsic secondary electron yield from the carbonaceous dust material is too low to explain the increase of electron density in the afterglow. It is, however, possible that the electrons charging the particles are weakly attached so that they may be released with high efficiency by ion bombardment due to field induced emission or by other mechanisms.

We treat the behavior of Bose-Einstein condensates in double square well potentials of both equal and different depths. For even depth, symmetry preserving solutions to the relevant nonlinear Schrödinger equation are known, just as in the linear limit. When the nonlinearity is strong enough, symmetry breaking solutions also exist, side by side with the symmetric one. Interestingly, solutions almost entirely localized in one of the wells are known as an extreme case. Here we outline a method for obtaining all these solutions for repulsive interactions. The bifurcation point at which, for critical nonlinearity, the asymmetric solutions branch off from the symmetry preserving ones is found analytically. We also find this bifurcation point and treat the solutions generally via a Josephson junction model. When the confining potential is in the form of two wells of different depth, interesting phenomena appear. This is true of both the occurrence of the bifurcation point for the static solutions and also of the dynamics of phase and amplitude varying solutions. Again a generalization of the Josephson model proves useful. The stability of solutions is treated briefly.

We present a mesoscopic model, based on the Boltzmann equation, for the interaction between a solid wall and a nonideal fluid. We present an analytic derivation of the contact angle in terms of the surface tension between the liquid-gas, the liquid-solid, and the gas-solid phases. We study the dependency of the contact angle on the two free parameters of the model, which determine the interaction between the fluid and the boundaries, i.e. the equivalent of the wall density and of the wall-fluid potential in molecular dynamics studies. We compare the analytical results obtained in the hydrodynamical limit for the density profile and for the surface tension expression with the numerical simulations. We compare also our two-phase approach with some exact results obtained by E. Lauga and H. Stone [J. Fluid. Mech. 489, 55 (2003)] and J. Philip [Z. Angew. Math. Phys. 23, 960 (1972)] for a pure hydrodynamical incompressible fluid based on Navier-Stokes equations with boundary conditions made up of alternating slip and no-slip strips. Finally, we show how to overcome some theoretical limitations connected with the discretized Boltzmann scheme proposed by X. Shan and H. Chen [Phys. Rev. E 49, 2941 (1994)] and we discuss the equivalence between the surface tension defined in terms of the mechanical equilibrium and in terms of the Maxwell construction.

We present the macroscopic equations for polar nematic liquid crystals. We consider the case where one has both, the usual nematic director, $\widehat{\mathbf{n}}$, characterizing quadrupolar order as well as the macroscopic polarization, $\mathbf{P}$, representing polar order, but where their directions coincide and are rigidly coupled. In this case one has to choose $\mathbf{P}$ as the independent macroscopic variable. Such equations are expected to be relevant in connection with nematic phases with unusual properties found recently in compounds composed of banana-shaped molecules. Among the effects predicted, which are absent in conventional nematic liquid crystals showing only quadrupolar order, are pyro-electricity and its analogs for density and for concentration in mixtures as well as a flow alignment behavior, which is more complex than in usual low molecular weight nematics. We also discuss the formation of defect structures expected in such systems.

We formulate a coarse-grained mean-field approach to study the dynamics of the flexible ring polymer in any given obstacle (gel or melt) environment. The similarity of the static structure of the ring polymer with that of the ideal randomly branched polymer is exploited in formulating the dynamical model using aspects of the pom-pom model for branched polymers. The topological constraints are handled via the tube model framework. Based on our formulation we obtain expressions for diffusion coefficient $D$, relaxation times $\tau$, and dynamic structure factor $g(\mathbf{k},t)$. Further, based on the framework we develop a molecular theory of linear viscoelasticity for ring polymers in a given obstacle environment and derive the expression for the relaxation modulus $G\left(t\right)$. The predictions of the theoretical model are in agreement with previously proposed scaling arguments and in qualitative agreement with the available experimental results for the melt of rings.

We report numerical mean-field results on the quasichemical level of approximation that describe adsorption of reversible supramolecular polymers at a flat interface. Emphasis is laid on the regime of strong adsorption from a dilute solution. There are two differences with respect to macromolecular polymer adsorption: (i) adsorption sets in at relatively high monomer concentrations of the surrounding solution, and (ii) the surface is filled within a much narrower concentration range. Contrary to macromolecular polymers, supramolecular polymers can therefore be desorbed by dilution of the equilibrium solution by solvent within an experimentally accessible concentration window. Based on simple thermodynamic arguments, we provide a quantitative explanation why supramolecular polymers adsorb at relatively high concentrations. Moreover, we discuss the (by comparison) narrow concentration window wherein filling of the surface occurs. This is attributed to the cooperative nature of supramolecular polymer adsorption. The degree of cooperativity is quantified by means of the Hill parameter $n$.

A stressed thin film on a soft substrate can develop complex wrinkle patterns. The onset of wrinkling and initial growth is well described by a linear perturbation analysis, and the equilibrium wrinkles can be analyzed using an energy approach. In between, the wrinkle pattern undergoes a coarsening process with a peculiar dynamics. By using a proper scaling and two-dimensional numerical simulations, this paper develops a quantitative understanding of the wrinkling dynamics from initial growth through coarsening till equilibrium. It is found that, during the initial growth, a stress-dependent wavelength is selected and the wrinkle amplitude grows exponentially over time. During coarsening, both the wrinkle wavelength and amplitude increases, following a power-law scaling under uniaxial compression. More complicated dynamics is predicted under equibiaxial stresses, which starts with a faster coarsening rate before asymptotically approaching the same scaling under uniaxial stresses. At equilibrium, a parallel stripe pattern is obtained under uniaxial stresses and a chaotic labyrinth pattern under equibiaxial stresses. Under stresses of the same magnitude, the two patterns have the same average wavelength, but different amplitudes. It is noted that the dynamics of wrinkling, while analogous to other phase ordering phenomena, is distinct and rich under the effects of stress and substrate elasticity.

This paper is part of a project, the goal of which is the development of the optimal spatial distributions of the porosity and permeability of a large-scale porous medium by using complementary static and dynamic data for the medium. The data include limited measurements of the porosity, which the method honors (preserves) in the optimal model and utilizes its correlation function, together with the first-arrival (FA) times, at a certain number of receivers, of seismic waves that have propagated in the medium and the time dependence of the pressure of a fluid flowing in the medium. The method uses the simulated-annealing (SA) technique in order to develop the optimal model. In the present paper we utilize the porosity and FA times data in order to develop the optimal spatial distribution of the porosity. This is accomplished by combining the SA method with a simulator that solves for the numerical solution of the acoustic-wave equation from which the FA times are estimated, limited porosity, and FA times data. We show that the optimal model not only honors the data, but also provides accurate estimates of the porosities in the rest of the porous medium. The efficiency of the computations is discussed in detail.

We present experimental evidence backed up by numerical simulations that the steady-state vortex tangle created in He II by heat-transfer counterflow is strongly polarized. When the heater that generates the counterflow turbulence is switched off, the vortex tangle decays, the vortex lines randomize their spatial orientation and the tangle’s polarization decreases. The process of depolarization slows down the recovery of the transverse second sound signal which measures the vortex line density; at some values of parameters it even leads to a net decrease of the amplitude of the transverse second sound prior to reaching the universal $-3∕2$ power temporal law decay typical of classical homogeneous isotropic turbulence in a finite-sized channel.

The subgrid-scale (SGS) modeling of helical, isotropic turbulence in large eddy simulation is investigated by quantifying rates of helicity and energy cascade. Assuming Kolmogorov spectra, the Smagorinsky model with its traditional coefficient is shown to underestimate the helicity dissipation rate by about 40%. Several two-term helical models are proposed with the model coefficients calculated from simultaneous energy and helicity dissipation balance. The helical models are also extended to include dynamic determination of their coefficients. The models are tested a priori in isotropic steady helical turbulence. Together with the dynamic Smagorinsky model and the dynamic mixed model, they are also tested a posteriori in both decaying and steady isotropic helical turbulence by comparing results to direct numerical simulations (DNS). The a priori tests confirm that the Smagorinsky model underestimates SGS helicity dissipation, although quantitative differences with the predictions are observed due to the finite Reynolds number of the DNS. Also, in a posteriori tests improvement can be achieved for the helicity decay rate with the proposed models, compared with the Smagorinsky model. Overall, however, the effect of the new helical terms added to obtain the correct rate of global helicity dissipation is found to be quite small. Within the small differences, the various versions of the dynamic model provide the results closest to the DNS. The dynamic model’s good performance in capturing mean kinetic energy dissipation at the finite Reynolds number of the simulations appears to be the most important aspect in accounting also for accurate prediction of the helicity dissipation.

The present study concerns the dynamic radiation force on solid elastic spheres exerted by a plane wave with two frequencies (bichromatic wave) considering the nonlinearity of the fluid. Our approach is based on solving the wave scattering for the sphere in the quasilinear approximation within the preshock wave range. The dynamic radiation force is then obtained by integrating the component of the momentum flux tensor at the difference of the primary frequencies over the boundary of the sphere. Results reveal that effects of the nonlinearity of the fluid play a major role in dynamic radiation force leading it to a parametric amplification regime. The developed theory is used to calculate the dynamic radiation force on three different solid spheres (aluminum, silver, and tungsten). Resonances are observed in the spectrum of the force on the spheres. They have larger amplitude and better shape than resonances present in static radiation force.

We construct asymptotic arguments for the relative efficiency of rejection-free Monte Carlo (MC) methods compared to the standard MC method. We find that the efficiency is proportional to $\exp \left(\mathrm{const}\beta \right)$ in the Ising, $\sqrt{\beta }$ in the classical XY, and $\beta$ in the classical Heisenberg spin systems with inverse temperature $\beta$, regardless of the dimension. The efficiency in hard particle systems is also obtained, and found to be proportional to $({\rho }_{\mathrm{cp}}-\rho {)}^{-d}$ with the closest packing density ${\rho }_{\mathrm{cp}}$, density $\rho$, and dimension $d$ of the systems. We construct and implement a rejection-free Monte Carlo method for the hard-disk system. The RFMC has a greater computational efficiency at high densities, and the density dependence of the efficiency is as predicted by our arguments.

We study the clustering of passive, noninteracting particles moving under the influence of a fluctuating field and random noise, in one and two dimensions. The fluctuating field in our case is provided by surfaces governed by the Kardar-Parisi-Zhang (KPZ) and the Edwards-Wilkinson (EW) equations, and the sliding particles follow the local surface slope. As the KPZ equation can be mapped to the noisy Burgers equation, the problem translates to that of passive scalars in a Burgers fluid. Monte Carlo simulations on discrete lattice models reveal very strong clustering of the passive particles for all sorts of dynamics under consideration. The resulting strong clustering state is defined using the scaling properties of the two point density-density correlation function. Our simulations show that the state is robust against changing the ratio of update speeds of the surface and particles. We also solve the related equilibrium problem of a stationary surface and finite noise, well known as the Sinai model for random walkers on a random landscape. For this problem, we obtain analytic results which allow closed form expressions to be found for the quantities of interest. Surprisingly, these results for the equilibrium problem show good agreement with the nonequilibrium KPZ problem.

We compare the results of kinetic Monte Carlo (KMC) simulations of a point-island model of irreversible nucleation and growth in four dimensions (4D) with the corresponding mean-field (MF) rate-equation predictions for the monomer density, island density, island-size distribution (ISD), capture-number distribution (CND), and capture-zone distribution (CZD), in order to determine the critical dimension $d_c$ for mean-field behavior. The asymptotic behavior is studied as a function of the fraction of occupied sites (coverage) and the ratio $D∕F$ of the monomer hopping rate $D$ to the (per site) monomer creation rate $F$. Excellent agreement is found between our KMC simulation results and the MF rate equation results for the average island and monomer densities. For large $D∕F$, the scaled CND and CZD do not depend on island size, in good agreement with the MF prediction, while the scaled ISD also agrees well with the MF prediction except for a slight difference at the peak values. Coupled with previous results obtained in $d=3$, these results indicate that for growth in the point-island regime, the upper critical dimension for irreversible cluster nucleation and growth is equal to 4.

The equilibrium texture of nematic shells is studied as a function of their thickness. For ultrathin shells the ground state has four short $\frac{1}{2}$ disclination lines but, as the thickness of the film increases, a three-dimensional escaped configuration composed of two pairs of half-hedgehogs becomes energetically favorable. We derive an exact solution for the nematic ground state in the one Frank constant approximation and study the stability of the corresponding texture against thermal fluctuations.

We compute the quadrupolar approximation to the excluded-volume interaction between hard spherocuboids, which applies to both platelets and spheroplatelets as special cases. We show that this approximation can be written as the superposition of two London interactions: one attractive and the other repulsive. This conclusion also proves why the phase diagram for the excluded-volume interaction of spherocuboids is expected to feature a direct isotropic-to-biaxial transition at a single Landau point.

The Yakushevich model of DNA torsion dynamics supports soliton solutions, which are supposed to be of special interest for DNA transcription. In the discussion of the model, one usually adopts the approximation ${\ell }_0\to 0$, where ${\ell }_0$ is a parameter related to the equilibrium distance between bases in a Watson-Crick pair. Here we analyze the Yakushevich model without ${\ell }_0\to 0$. The model still supports soliton solutions indexed by two winding numbers $(n,m)$; we discuss in detail the fundamental solitons, corresponding to winding numbers (1,0) and (0,1) respectively.

We demonstrate that wetting effects at moving contact lines have a strong impact in viscous fingering patterns. Experiments in a rotating Hele-Shaw (HS) cell, dry or prewetted, show consistent morphological differences. When the wetting fluid invades a dry region, contact angle dynamics yield a kinetic contribution to the interface pressure drop that scales with capillary number as ${\mathrm{Ca}}^{2∕3}$ but is significantly larger than the Park-Homsy kinetic correction. Numerical results are in very good agreement with experiments and show that standard HS equations work best for prewetted cells.