The homogeneous and heterogeneous nucleation of a Lennard-Jones liquid is investigated using the umbrella sampling method. The free energy cost of forming a nucleating droplet is determined as a function of the quench depth, and the saddle point nature of the droplets is verified using an intervention technique. The structure and symmetry of the nucleating droplets are found for a range of temperatures. We find that for deep quenches the nucleating droplets become more anisotropic and diffuse with no well-defined core or surface. The environment of the nucleating droplets forms randomly stacked hexagonal planes. This behavior is consistent with a spinodal nucleation interpretation. We also find that the free energy barrier for heterogeneous nucleation is a minimum when the lattice spacing of the impurity equals the lattice spacing of the equilibrium crystalline phase. If the lattice spacing of the impurity is different, the crystal grows into the bulk instead of wetting the impurity.

In an important paper, Newman [Phys. Rev. E66, 016128 (2002)] claimed that a general network-based stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to a bond percolation model, where the bonds are the edges of the contact network and the bond occupation probability is equal to the marginal probability of transmission from an infected node to a susceptible neighbor. In this paper, we show that this isomorphism is incorrect and define a semidirected random network we call the epidemic percolation network that is exactly isomorphic to the SIR epidemic model in any finite population. In the limit of a large population, (i) the distribution of (self-limited) outbreak sizes is identical to the size distribution of (small) out-components, (ii) the epidemic threshold corresponds to the phase transition where a giant strongly connected component appears, (iii) the probability of a large epidemic is equal to the probability that an initial infection occurs in the giant in-component, and (iv) the relative final size of an epidemic is equal to the proportion of the network contained in the giant out-component. For the SIR model considered by Newman, we show that the epidemic percolation network predicts the same mean outbreak size below the epidemic threshold, the same epidemic threshold, and the same final size of an epidemic as the bond percolation model. However, the bond percolation model fails to predict the correct outbreak size distribution and probability of an epidemic when there is a nondegenerate infectious period distribution. We confirm our findings by comparing predictions from percolation networks and bond percolation models to the results of simulations. In the Appendix, we show that an isomorphism to an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model.

We consider the photoacoustic effect for multiply scattered light in a random medium. Within the accuracy of the diffusion approximation to the radiative transport equation, we present a general analysis of the sensitivity of a photoacoustic wave to the presence of one or more small absorbing objects. Applications to tumor detection by photoacoustic imaging are suggested.

We present a hybrid protocol designed to couple the dynamics of a nanoscopic region of liquid described at atomistic level with a fluctuating hydrodynamics description of the surrounding liquid. The hybrid technique is based on the exchange of fluxes and it is shown to respect the conservation laws of fluid mechanics. This fact allows us to solve unsteady flows involving shear and sound waves crossing the interface of both domains. In equilibrium we find perfect agreement with the grand-canonical ensemble at low and moderate densities, while within the nanoscopic volumes considered, mass fluctuation (both in hybrid and full MD simulations) becomes slightly larger than predicted by the thermodynamic limit. Stress fluctuations across the hybrid interface are shown to have a seamless profile. Nonequilibrium scenarios involving shear (startup of Couette flow) and longitudinal flow (sound waves) are also illustrated.

Recently we have introduced an inductive reasoning game of voluntary yearly vaccination to establish whether or not a population of individuals acting in their own self-interest would be able to prevent influenza epidemics. Here, we analyze our model to describe the dynamics of the collective yearly vaccination uptake. We discuss the mean-field equations of our model and first order effects of fluctuations. We explain why our model predicts that severe epidemics are periodically expected even without the introduction of pandemic strains. We find that fluctuations in the collective yearly vaccination uptake induce severe epidemics with an expected periodicity that depends on the number of independent decision makers in the population. The mean-field dynamics also reveal that there are conditions for which the dynamics become robust to the fluctuations. However, the transition between fluctuation-sensitive and fluctuation-robust dynamics occurs for biologically implausible parameters. We also analyze our model when incentive-based vaccination programs are offered. When a family-based incentive is offered, the expected periodicity of severe epidemics is increased. This results from the fact that the number of independent decision makers is reduced, increasing the effect of the fluctuations. However, incentives based on the number of years of prepayment of vaccination may yield fluctuation-robust dynamics where severe epidemics are prevented. In this case, depending on prepayment, the transition between fluctuation-sensitive and fluctuation-robust dynamics may occur for biologically plausible parameters. Our analysis provides a practical method for identifying how many years of free vaccination should be provided in order to successfully ameliorate influenza epidemics.

We report hybrid lattice Boltzmann (HLB) simulations of the hydrodynamics of an active nematic liquid crystal sandwiched between confining walls with various anchoring conditions. We confirm the existence of a transition between a passive phase and an active phase, in which there is spontaneous flow in the steady state. This transition is attained for sufficiently “extensile” rods, in the case of flow-aligning liquid crystals, and for sufficiently “contractile” ones for flow-tumbling materials. In a quasi-one-dimensional geometry, deep in the active phase of flow-aligning materials, our simulations give evidence of hysteresis and history-dependent steady states, as well as of spontaneous banded flow. Flow-tumbling materials, in contrast, rearrange themselves so that only the two boundary layers flow in steady state. Two-dimensional simulations, with periodic boundary conditions, show additional instabilities, with the spontaneous flow appearing as patterns made up of “convection rolls.” These results demonstrate a remarkable richness (including dependence on anchoring conditions) in the steady-state phase behavior of active materials, even in the absence of external forcing; they have no counterpart for passive nematics. Our HLB methodology, which combines lattice Boltzmann for momentum transport with a finite difference scheme for the order parameter dynamics, offers a robust and efficient method for probing the complex hydrodynamic behavior of active nematics.

We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the “strong” transition) [Bhattacharya et al., Phys. Rev. Lett. 85, 4852 (2000)], and the second by considering phase-space densities (the “weak” transition) [Greenbaum et al., Chaos 15, 033302 (2005)]. On the face of it these conditions appear rather different. We show, however, that in the semiclassical regime, in which the action of the system is large compared to $\hslash$, and the measurement noise is small, they both offer an essentially equivalent local picture. Within this regime, the weak conditions dominate while in the opposite regime where the action is not much larger than $\hslash$, the strong conditions dominate.

We study the saturation near threshold of the axisymmetric magnetorotational instability (MRI) of a viscous, resistive, incompressible fluid in a thin-gap Taylor-Couette configuration. A vertical magnetic field, Keplerian shear, and no-slip conducting radial boundary conditions are adopted. The weakly nonlinear theory leads to a real Ginzburg-Landau equation for the disturbance amplitude, as in our previous idealized analysis. For small magnetic Prandtl number $({\mathcal{P}}_{\mathrm{m}}\ll 1)$, the saturation amplitude scales as ${\mathcal{P}}_{\mathrm{m}}^{2∕3}$ while the magnitude of angular momentum transport scales as ${\mathcal{P}}_{\mathrm{m}}^{4∕3}$. The difference from the previous scalings (proportional to ${\mathcal{P}}_{\mathrm{m}}^{1∕2}$ and ${\mathcal{P}}_{\mathrm{m}}$ respectively) is attributed to the emergence of radial boundary layers. Away from those, steady-state nonlinear saturation is achieved through a modest reduction in the destabilizing shear. These results will be useful in understanding MRI laboratory experiments and associated numerical simulations.

We show that chaotic states situated in the proximity of periodic windows in bifurcation diagrams are eligible for the observation of coherence resonance. In particular, additive Gaussian noise of appropriate intensity can enhance the temporal order in such chaotic states in a resonant manner. Results obtained for the logistic map and the Lorenz equations suggest that the presented mechanism of coherence resonance is valid beyond particularities of individual systems. We attribute the findings to the increasing attraction of imminent periodic orbits and the ability of noise to anticipate their existence and use a modified wavelet analysis to support our arguments.

We investigate the quantum walk and the quantum kicked rotor in resonance subjected to noise with a Lévy waiting time distribution. We find that both systems have a sub-ballistic wave function spreading as shown by a power-law tail of the standard deviation.

We present a systematic theory of formation of the universal annihilation catastrophe which develops in an open system where species $A$ and $B$ diffuse from the bulk of a restricted medium and die on its surface (desorb) by the reaction $A+B\to 0$. This phenomenon arises in the diffusion-controlled limit as a result of self-organizing explosive growth (drop) of the surface concentrations of, respectively, slow and fast particles (concentration explosion), and manifests itself in the form of an abrupt singular jump of the desorption flux relaxation rate. As striking results we find the dependences of time and amplitude of the catastrophe on the initial particle number, and answer the basic questions of when and how universality is achieved.

Combining analytical and numerical methods, we study within the framework of the homogeneous nonlinear Boltzmann equation a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the method presented in a previous paper [J. Stat. Phys. 124, 549 (2006)] and extend our results to a different heating mechanism: namely, a deterministic nonlinear friction force. We derive analytically the high-energy tail of the velocity distribution and compare the theoretical predictions with high-precision numerical simulations. Stretched exponential forms are obtained when the nonequilibrium steady state is stable. We derive subleading corrections and emphasize their relevance. In marginal stability cases, power-law behaviors arise, with exponents obtained as the roots of transcendental equations. We also consider some simple Bhatnagar-Gross-Krook models, driven by similar heating devices, to test the robustness of our predictions.

A theory of chiral lipid membranes is proposed on the basis of a concise free energy density which includes the contributions of the bending and the surface tension of membranes, as well as the chirality and orientational variation of tilting molecules. This theory is consistent with the previous experiments [J.M. Schnur et al., Science 264, 945 (1994); M.S. Spector et al., Langmuir 14, 3493 (1998); Y. Zhao, et al., Proc. Natl. Acad. Sci. USA 102, 7438 (2005)] on self-assembled chiral lipid membranes of ${\mathrm{DC}}_{8,9}\mathrm{PC}$. A torus with the ratio between its two generated radii larger than $\sqrt{2}$ is predicted from the Euler-Lagrange equations. It is found that tubules with helically modulated tilting state are not admitted by the Euler-Lagrange equations and that they are less energetically favorable than helical ripples in tubules. The pitch angles of helical ripples are theoretically estimated to be about 0° and 35°, which are close to the most frequent values 5° and 28° observed in the experiment [N. Mahajan et al., Langmuir 22, 1973 (2006)]. Additionally, the present theory can explain twisted ribbons of achiral cationic amphiphiles interacting with chiral tartrate counterions. The ratio between the width and pitch of twisted ribbons is predicted to be proportional to the relative concentration difference of left- and right-handed enantiomers in the low relative concentration difference region, which is in good agreement with the experiment [R. Oda et al., Nature (London) 399, 566 (1999)].

We study phase separation in thin films using a model based on the Navier-Stokes Cahn-Hilliard equations in the lubrication approximation, with a van der Waals potential to account for substrate-film interactions. We solve the resulting thin-film equations numerically and compare to experimental data. The model captures the qualitative features of real phase-separating fluids, in particular, how concentration gradients produce film thinning and surface roughening. The ultimate outcome of the phase separation depends strongly on the dynamical back reaction of concentration gradients on the flow, an effect we demonstrate by applying a shear stress at the film’s surface. When the back reaction is small, the phase domain boundaries align with the direction of the imposed stress, while for larger back-reaction strengths, the domains align in the perpendicular direction.

We introduce a method to detect and quantify the asymmetry of the coupling between two interacting systems based on their recurrence properties. This method can detect the direction of the coupling in weakly as well as strongly coupled systems. It even allows detecting the asymmetry of the coupling in the more challenging case of structurally different systems and it is very robust against noise. We also address the problem of detecting the asymmetry of the coupling in passive experiments, i.e., when the strength of the coupling cannot be systematically changed, which is of great relevance for the analysis of experimental time series.

In this paper we study synchronization in linearly coupled time-delayed systems. We first consider coupled nonidentical Ikeda systems with a square wave coupling rate. Using the theory of the time-delayed equation, we derive less restrictive synchronization conditions than those resulting from the Krasovskii-Lyapunov theory [Yang Kuang, Delay Differential Equations (Academic Press, New York, 1993)]. Then we consider a wide class of nonlinear nonidentical time-delayed systems. We also propose less restrictive synchronization conditions in an approximative sense, even if the coefficients in the linear time-delayed equation on the synchronization error are time dependent. Theoretical analysis and numerical simulations fully verify our main results.

The permeability of geological formations which contain fractures with a power-law size distribution is addressed numerically by solving the coupled Darcy equations in the fractures and in the surrounding porous medium. Two reduced parameters are introduced which allow for a unified description over a very wide range of the fracture characteristics, including their shape, density, size distribution, and possibly size-dependent permeability. Two general models are proposed for loose and dense fracture networks, and they provide a good representation of the numerical data throughout the investigated parameter range.

Theoretical results for the electrical conductivity of noble gas plasmas are presented in comparison with experiment. The composition is determined within a partially ionized plasma model. The conductivity is then calculated using linear response theory, in which the relevant scattering mechanisms of electrons from ions, electrons, and neutral species are taken into account. In particular, the Ramsauer-Townsend effect in electron-neutral scattering is discussed and the importance of a correct description of the Coulomb logarithm in electron scattering by charged particles is shown. A detailed comparison with recent experiments on argon and xenon plasmas is given and results for helium and neon are also revisited. Excellent agreement between theory and experiment is observed, showing considerable improvement upon previous calculations.

The London ground-state energy formula as a function of number density for a system of identical boson hard spheres, corrected for the reduced mass of a pair of particles in a “sphere-of-influence” picture, and generalized to fermion hard-sphere systems with two and four intrinsic degrees of freedom, has a double-pole at the ultimate regular (or periodic, e.g., face-centered-cubic) close-packing density usually associated with a crystalline branch. Improved fluid branches are constructed based upon exact, field-theoretic perturbation-theory low-density expansions for many-boson and many-fermion systems, extrapolated to intermediate densities via Padé and other approximants, but whose ultimate density is irregular or random closest close-packing as suggested in studies of a classical system of hard spheres. Results show substantially improved agreement with the best available Green-function Monte Carlo and diffusion Monte Carlo simulations for bosons, as well as with ladder, variational Fermi hypernetted chain, and so-called $L$-expansion data for two-component fermions.

We deal with a biophysical description of antitumor antiangiogenic therapies. In particular, by means of some simple models, we study the possible effects of the delay between the drug consumption by endothelial cells and their death on the outcome of the therapy. We have found that this time lag implies an increase in the minimal dose guaranteeing tumor eradication and, if the delay is greater than a meaningful threshold, it may preclude the total regression. These results might be of interest in better understanding the causes underlying the contradictory literature on the clinical trials of antiangiogenic therapies.