Nonlinear wave motion is studied in a symmetric, continuously stratified, smoothed three-layer fluid in the framework of the fully nonlinear Euler equations under the Boussinesq approximation. The weakly nonlinear limit is discussed in which the governing equations can be reduced to the fully integrable modified Korteweg–de Vries equation. For some choices of the layer thicknesses the cubic nonlinear term is positive and the modified Korteweg–de Vries equation has soliton and breather solutions. Using such a stratification, the Euler equations are solved numerically using a sign-variable, initial disturbance. Breathers were generated for several forms of the initial disturbance. The breathers have moderate amplitude and to a good approximation can be described by the modified Korteweg–de Vries equation. As far as we know this is the first presentation of a breather in numerical simulations using the full nonlinear Euler equations for a stratified fluid.

Contrary to the main conclusion of Simonetti [Phys. Rev. E 73, 036619 (2006)], we maintain that multiple scattering (MS) is not the “key” for subwavelength detection. Indeed, even with no MS between subwavelength structures, subwavelength detection is still possible. Our statement is numerically confirmed. A simple mathematical argument explains this result. From our point of view, the incorrect conclusion of Simonetti comes from a misinterpretation of the Picard’s theorem.

In a recent paper [F. Simonetti, Phys. Rev. E 73, 036619 (2006)], it is suggested that multiple scattering is the key to achieve subwavelength resolution imaging from far-field measurements. In support of this claim, the same paper also reports on an experiment in which a resolution better $\lambda ∕3$ is achieved, $\lambda$ being the wavelength of the probing wave. In a Comment [J. de Rosny and C. Prada, preceding paper, Phys. Rev. E. 75, 048601 (2007)], this argument is disputed and it is claimed that subwavelength resolution is possible under the Born approximation. However, in de Rosny and Prada the effect of measurement noise, which is central to the use of subwavelength resolution techniques in practice, is not considered. By means of an example similar to that discussed in de Rosny and Prada, this paper confirms that multiple scattering is indeed a “key” factor to achieve subwavelength resolution with real, noisy measurements.

We solve the ferromagnetic $q$-state Potts model on an inhomogeneous annealed network which mimics a random recursive graph. We find that this system has the inverted Berezinskii-Kosterlitz-Thouless (BKT) phase transition for any $q⩾1$, including the values $q⩾3$, where the Potts model normally shows a first order phase transition. We obtain the temperature dependences of the order parameter, specific heat, and susceptibility demonstrating features typical for the BKT transition. We show that in the entire normal phase, both the distribution of a linear response to an applied local field and the distribution of spin-spin correlations have a critical, i.e., power-law form.

Atomistic computer simulations are presented, consisting of droplets of model liquid crystal molecules wetting a generic crystalline surface. It is shown that the type of wetting that occurs is highly dependent on the value of the surface interaction parameter ${\epsilon }_{\mathrm{fs}}$, switching between partial wetting (no spreading) for ${\epsilon }_{\mathrm{fs}}=2.0$ to complete wetting for ${\epsilon }_{\mathrm{fs}}=2.5$. ${\epsilon }_{\mathrm{fs}}$ is the multiplicative factor which scales the well depth of the fluid-surface interaction energy. During complete wetting, the spreading occurs through the growth of a precursor layer, and a set of secondary terraces. The temperature affects the structure of the droplet, as might be expected when different phases are sampled, and also the shape of the spreading droplet, and the rate of spreading. In particular, in the smectic-$A$ phase at $350\mathrm{K}$, for values of ${\epsilon }_{\mathrm{fs}}$ just large enough to induce complete wetting, the precursor film assumes a diamond shape, with edges normal to the [110] directions in the crystal surface. It is shown that spreading occurs through diffusion across the surface, with the radius of the precursor layer increasing with the square root of time. Mass flow studies indicate that the spreading occurs by molecules cascading over the top of the droplet to feed the growing precursor layer. Calculations of contact angle relaxation are in qualitative agreement with experimental findings.

We have derived an approximate analytical expression for the static director distortion of a planar nematic layer subject to a magnetic field $H$ immediately above the critical Fréedericksz transition $H=H_c$. The layer contains a voltage-independent density of positively and negatively singly charged ionic species that interact with the flexoelectric and dielectric polarizations which appear when the director is distorted. The analytical solution is shown to correspond closely to a full numerical calculation when $H∕H_c=1.01$. The analytical approach allows a quantitative insight into how the mobile charge shields the polarization for different values of the elastic constants, the ionic density, the flexoelectric coefficients, and the layer thickness.

We investigate the domain structure of the pair contact process with diffusion (PCPD). PCPD is a stochastic reaction-diffusion model which evolves by the competition of two binary reactions, $2A\to 3A$ and $2A\to 0$. In addition, each particle diffuses isotropically, which leads to the bidirectional coupling between solitary particles and pairs. The spreading domain formed from localized activities in vacuum consists of two regions: The coupled region of size $R_p$ where pairs and solitary particles coexist and the uncoupled region of size $R_U$ where only solitary particles exist, respectively. The size of the whole domain $R$ is given as $R=R_p+R_U$. At criticality, $R_p$ and $R_U$ scale as $R_p\sim t^{1∕Z_p}$ and $R_U\sim t^{1∕Z_U}$ with $Z_U>Z_p$. We estimate $Z_p=1.61\left(1\right)$ and $Z_U=1.768\left(8\right)$. Hence the correction to the scaling of $R$, $Q=R_U∕R_p$ slowly decays extremely, which makes it practically impossible to identify the asymptotic scaling behavior of $R$. The double domain structure is another reason for the extremely slow approach to the asymptotic scaling regime of PCPD.

We study the distribution $P\left(\sigma \right)$ of the equivalent conductance $\sigma$ for Erdös-Rényi (ER) and scale-free (SF) weighted resistor networks with $N$ nodes. Each link has conductance $g\equiv e^{-ax}$, where $x$ is a random number taken from a uniform distribution between 0 and 1 and the parameter $a$ represents the strength of the disorder. We provide an iterative fast algorithm to obtain $P\left(\sigma \right)$ and compare it with the traditional algorithm of solving Kirchhoff equations. We find, both analytically and numerically, that $P\left(\sigma \right)$ for ER networks exhibits two regimes: (i) A low conductance regime for $\sigma <e^{-a{p}_c}$, where $p_c=1∕⟨k⟩$ is the critical percolation threshold of the network and $⟨k⟩$ is the average degree of the network. In this regime $P\left(\sigma \right)$ is independent of $N$ and follows the power law $P\left(\sigma \right)\sim {\sigma }^{-\alpha }$, where $\alpha =1-⟨k⟩∕a$. (ii) A high conductance regime for $\sigma >e^{-a{p}_c}$ in which we find that $P\left(\sigma \right)$ has strong $N$ dependence and scales as $P\left(\sigma \right)\sim f(\sigma ,a{p}_c∕N^{1∕3})$. For SF networks with degree distribution $P\left(k\right)\sim k^{-\lambda }$, $k_{min}\le k\le k_{max}$, we find numerically also two regimes, similar to those found for ER networks.

Many observations of the dynamics of pedestrian crowds, including various self-organization phenomena, have been successfully described by simple many-particle models. For ethical reasons, however, there is a serious lack of experimental data regarding crowd panic. Therefore, we have analyzed video recordings of the crowd disaster in Mina/Makkah during the Hajj in 1426H on 12 January 2006. They reveal two subsequent, sudden transitions from laminar to stop-and-go and “turbulent” flows, which question many previous simulation models. While the transition from laminar to stop-and-go flows supports a recent model of bottleneck flows [D. Helbing et al., Phys. Rev. Lett. 97, 168001 (2006)], the subsequent transition to turbulent flow is not yet well understood. It is responsible for sudden eruptions of pressure release comparable to earthquakes, which cause sudden displacements and the falling and trampling of people. The insights of this study into the reasons for critical crowd conditions are important for the organization of safer mass events. In particular, they allow one to understand where and when crowd accidents tend to occur. They have also led to organizational changes, which have ensured a safe Hajj in 1427H.

A simulation has been performed to reveal the detailed dynamics and statistical behavior of a Maxwell demon of the simplest kind, a trap door held over by a spring inside a box filled with gas molecules. The role of such a demon can be controlled by tuning Smoluchowski’s fluctuations. When the demon is in thermal equilibrium with the rest of the system, it fails to function as designed, and when it is separately subjected to a thermal bath with a different temperature, it creates a temperature or density gradient between the two chambers of the box it divides. As a Maxwell demon, the trap-door device creates more readily a density gradient than that of temperature.

Effective Hamiltonian models predict nonuniversal critical singularities for two-dimensional wetting transitions with marginal long-ranged forces. We test these predictions by studying interfacial delocalization transitions in an infinitely long Ising strip, of width $L$ (lattice spacings), with external fields that are long ranged and have opposite signs at each surface. Finite-size scaling suggests that the shift of the delocalization temperature $T_c\left(L\right)$ below the (semi-infinite) wetting temperature $T_w$ scales as $L^{-1∕{\beta }_s}$ with ${\beta }_s$ the adsorption critical exponent. Density-matrix renormalization-group methods allow us to study the behavior of $T_c\left(L\right)$ for $L$ up to several hundred lattice spacings. For short-ranged forces the method recovers the universal value of ${\beta }_s=1$ known from the exact solution. While marginal long-ranged forces strongly influence the finite-size scaling of $T_c\left(L\right)$, the extrapolated asymptotic value for the exponent ${\beta }_s$ does not appear to confirm the predicted nonuniversality, but instead approaches the same universal value representative of systems with short-ranged forces.

We consider the classical evolution of a lattice of nonlinear coupled oscillators for a special case of initial conditions resembling the equilibrium state of a macroscopic thermal system at the critical point. The displacements of the oscillators define initially a fractal measure on the lattice associated with the scaling properties of the order parameter fluctuations in the corresponding critical system. Assuming a sudden symmetry breaking (quench), leading to a change in the equilibrium position of each oscillator, we investigate in some detail the deformation of the initial fractal geometry as time evolves. In particular, we show that traces of the critical fractal measure can be sustained for large times, and we extract the properties of the chain that determine the associated time scales. Our analysis applies generally to critical systems for which, after a slow developing phase where equilibrium conditions are justified, a rapid evolution, induced by a sudden symmetry breaking, emerges on time scales much shorter than the corresponding relaxation or observation time. In particular, it can be used in the fireball evolution in a heavy-ion collision experiment, where the QCD critical point emerges, or in the study of evolving fractals of astrophysical and cosmological scales, and may lead to determination of the initial critical properties of the Universe through observations in the symmetry-broken phase.

Transverse paramagnetic particle chains parametrically driven by a magnetic ratchet potential rupture and heal upon collision with an obstacle. The overdamped transverse dynamics is frozen during the time the particles stay in the ratchet potential wells and kicked during the time the particles hop to the next well. On time scales large compared to the parametric modulation period the healing of the hole in the chain is determined by dipolar repulsion and hydrodynamic friction of the paramagnetic particles.

The specific heat is frequency dependent in highly viscous liquids. By solving the full one-dimensional thermoviscoelastic problem analytically it is shown that, because of thermal expansion and the fact that mechanical stresses relax on the same time scale as the enthalpy relaxes, the plane thermal-wave method does not measure the isobaric frequency-dependent specific heat $c_p\left(\omega \right)$. This method rather measures a “longitudinal” frequency-dependent specific heat, a quantity defined and detailed here that is in between $c_p\left(\omega \right)$ and $c_V\left(\omega \right)$. This result means that no reliable wide-frequency measurements of $c_p\left(\omega \right)$ on liquids approaching the calorimetric glass transition exist. We briefly discuss consequences for experiment.

Two universal reconstruction methods for photoacoustic (also called optoacoustic or thermoacoustic) computed tomography are derived, applicable to an arbitrarily shaped detection surface. In photoacoustic tomography acoustic pressure waves are induced by illuminating a semitransparent sample with pulsed electromagnetic radiation and are measured on a detection surface outside the sample. The imaging problem consists in reconstructing the initial pressure sources from those measurements. The first solution to this problem is based on the time reversal of the acoustic pressure field with a second order embedded boundary method. The pressure on the arbitrarily shaped detection surface is set to coincide with the measured data in reversed temporal order. In the second approach the reconstruction problem is solved by calculating the far-field approximation, a concept well known in physics, where the generated acoustic wave is approximated by an outgoing spherical wave with the reconstruction point as center. Numerical simulations are used to compare the proposed universal reconstruction methods with existing algorithms.

Weierstrass’s theory is a standard qualitative tool for single degree of freedom equations, used in classical mechanics and in many textbooks. In this Brief Report we show how a simple generalization of this tool makes it possible to identify some differential equations for which compact and even semicompact traveling solitary waves exist. In the framework of continuum mechanics, these differential equations correspond to bulk shear waves for a special class of constitutive laws.

We present results of simulations that predict the phases formed by the self-assembly of model nanospheres functionalized with a single polymer “tether,” including double gyroid, perforated lamella, and crystalline bilayer phases. We show that microphase separation of the immiscible tethers and nanospheres causes confinement of the nanoparticles, which promotes local icosahedral packing that in turn stabilizes the gyroid. We present a new metric for determining the local arrangement of particles based on spherical harmonic “fingerprints,” which we use to quantify the extent of icosahedral ordering.

We investigate the order parameter of the standard Ising lattice gas and driven Ising lattice gas models. The sub-block order parameter is introduced to these conserved models as an order parameter using block distribution functions. We also introduce the sub-block order parameter of damage using the block distribution functions of damage. We measure the sub-block order parameters using the Metropolis and heat-bath rates. These order parameters work well for the non-equilibrium-conserved model as well as the equilibrium-conserved model. We obtain the critical exponent of order parameter $\beta =1∕8$ for the standard Ising lattice gas and $\beta =1∕2$ for a driven Ising lattice gas using the Metropolis and heat-bath rates.

We consider a sharp interface kinetic model of phase transitions accompanied by elastic strain, together with its phase-field realization. Quantitative results for the steady-state growth of a new phase in a strip geometry are obtained, and different pattern formation processes in this system are investigated.

Nematic elastomers containing azobenzene chromophores are activated upon photoabsorption. We study the surface deformation of such elastomers under striped illumination. For an arbitrary orientation of the nematic axis, we obtain an analytical solution to the problem via a phenomenological continuum model. Numerical computations indicate that the profile of the deformed surface depends not only on the stripe width but also on the orientation of the nematic axis. The result may provide a mechanism to manipulate the surface topography of elastomers.