A simple Langevin approach is used to study stationary properties of the Peyrard-Bishop-Dauxois model for DNA, allowing known properties to be recovered in an easy way. Results are shown for the denaturation transition in homogeneous samples, for which some implications, so far overlooked, of an analogy with equilibrium wetting transitions are highlighted. This analogy implies that the order parameter, asymptotically, exhibits a second-order transition even if it may be very abrupt for nonzero values of the stiffness parameter. Not surprisingly, we also find that, for heterogeneous DNA, within this model the largest bubbles in the premelting stage appear in adenine-thymine-rich regions, while we suggest the possibility of some sort of not strictly local effects owing to the merging of bubbles.

We present the deformation pathway of critically charged glycol and water droplets from the onset of the Rayleigh instability and compare it to numerical results, obtained for perfectly conducting inviscid droplets. In this simple model presented here, the time evolution of the droplet shape is given by the velocity potential equation. The Laplace equation for the velocity potential is solved by expanding the potential onto harmonic functions. For the part of the pathway dominated by electrostatic pressure, the calculations reproduce the experimental data nicely, obtained for both, glycol and water microdroplets. We find that the droplet shape and in particular the tips, just before charge emission, are well fitted by a lemon shape. We stress that the tip is tangent to a cone of $39°$ and thus significantly narrower than a Taylor cone.

Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description is reasonable and the amplitude equation holds. The linear and nonlinear analyses of the amplitude equation and the numerical computations show that such vibration stabilizes the film against dewetting and rupture.

An important paradigm in pneumatic atomization is the production of droplet sizes in the micron and submicron range, while achieving high energy efficiency by means of simple atomizer designs. Flow focusing (FF) and flow blurring (FB) [A. M. Gañán-Calvo, Appl. Phys. Lett.86, 214101 (2005).] are advancements toward this goal. Both FF and FB feature a fundamental macroscopic soft length scale, e.g., the diameter of the liquid stream formed at a discharge orifice by conversion of pressure into liquid kinetic energy. Droplet diameter distribution data compiled from many experiments reveal that turbulent flow regimes occur in both FF and FB. In FF, like in other jet-based droplet generation techniques, the jet breakup becomes asymmetric for Weber numbers over a transitional one (approximately 20 in FF), becoming turbulent through nonlinear interactions with the gas, downstream of the discharge orifice, for large enough Weber numbers. In FB, the liquid and gas phases interact inherently in a turbulent manner: air accelerates radially and implosively toward the liquid exiting a feeding tube, and mixes with it in a region immediately preceding discharge into ambient air. In our model, droplets form by the action of turbulent pressure fluctuations present in both phases, and a resulting droplet diameter distribution is obtained when coagulation and breakup events of the liquid blobs equilibrate. When the large scale of the turbulent inertial range is taken to be the fundamental soft scale, the model predicts a lower bound to the experimentally determined droplet volume median diameters. On the other hand, the histograms reflect the existence of additional hard length scales imposed by the atomizer outlet geometry.

Linear stability and the nonmodal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the uniform shear flow with constant viscosity, and (b) the nonuniform shear flow with stratified viscosity. Both mean flows are linearly unstable for a range of supersonic Mach numbers $\left(M\right)$. For a given $M$, the critical Reynolds number (Re) is significantly smaller for the uniform shear flow than its nonuniform shear counterpart; for a given Re, the dominant instability (over all streamwise wave numbers, $\alpha$) of each mean flow belongs to different modes for a range of supersonic $M$. An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean flow to perturbations. It is shown that the energy transfer from mean flow occurs close to the moving top wall for “mode I” instability, whereas it occurs in the bulk of the flow domain for “mode II.” For the nonmodal transient growth analysis, it is shown that the maximum temporal amplification of perturbation energy, $G_{\max }$, and the corresponding time scale are significantly larger for the uniform shear case compared to those for its nonuniform counterpart. For $\alpha =0$, the linear stability operator can be partitioned into $\mathcal{L}\sim \overline{\mathcal{L}}+{\mathrm{Re}}^2{\mathcal{L}}_p$, and the Re-dependent operator ${\mathcal{L}}_p$ is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: $G(t∕\mathrm{Re})\sim {\mathrm{Re}}^2$. In contrast, the dominance of ${\mathcal{L}}_p$ is responsible for the invalidity of this scaling law in nonuniform shear flow. An inviscid reduced model, based on Ellingsen-Palm-type solution, has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and nonmodal instability, it is shown that the viscosity stratification of the underlying mean flow would lead to a delayed transition in compressible Couette flow.

We experimentally investigated statistical properties of side branches of quasi-two-dimensional $\mathrm{N}{\mathrm{H}}_4\mathrm{Cl}$ dendritic crystals. The height distributions of the side branches and their number density exhibit scale-invariant power laws. The results are in good agreement with the results of numerical simulations and theories of diffusion-limited needle growth. Our scaling exponents are independent of supersaturation and the statistical properties are universal in dendrites.

The one-dimensional dynamics of a dimer consisting of two harmonically coupled components is considered. The mutual distance between the dimer components plays the role of an internal degree of freedom. Both components are in contact with the same heat bath and are coupled to a spatially periodic, symmetric potential, whose amplitude is modulated periodically in time and whose coupling strength is different for the two components. In the absence of any external bias, a ratchet effect (directed transport) arises generically unless the mutual coupling of the dimer components tends to zero or infinity. In other words, the ratchet effect is generated by the internal degree of freedom. An accurate analytical approximation for the dimer’s velocity and diffusion coefficient is obtained. The velocity of the system is maximized by adding an optimal amount of noise and by tuning the driving frequency to an optimal value. Furthermore, there exists an optimal coupling strength at which the velocity is the largest.

We report the analytical study of a class of chemical reactions described as birth-and-death stochastic processes ruled by a master equation compatible with the mass action law of chemical kinetics. We solve analytically this master equation to find the generating functions of the fluctuating fluxes and of the Lebowitz-Spohn action functional. These generating functions are explicitly shown to obey fluctuation theorems. In the case of fluxes, we derive relations for the nonlinear response coefficients, extending Onsager’s reciprocity relations. Moreover, symmetry relations reminiscent of the fluctuation theorem are obtained for the finite-time probability distributions of the fluxes. The temporal disorder of the stochastic process is also characterized and related to the thermodynamic entropy production.

A bundle of many fibers with stochastically distributed breaking thresholds for the individual fibers is considered as a model of composite materials. The bundle is loaded until complete failure, to capture the failure scenario of composite materials under external load. The fibers are assumed to share the load equally, and to obey Hookean elasticity right up to the breaking point. We determine the distribution of bursts in which an amount of energy $E$ is released. The energy distribution follows asymptotically a universal power law $E^{-5/2}$, for any statistical distribution of fiber strengths. A similar power law dependence is found in some experimental acoustic emission studies of loaded composite materials.

We report on a study of the influence of a magnetic field on the nematic phase and the isotropic-to-nematic (IN) phase transition of hard colloidal gibbsite platelets. We find direct visual evidence of a shift of the IN transition to lower concentrations due to the magnetic field. The nematic phase readily aligns when contained between two parallel flat glass walls, with homeotropic orientation. This well-defined surface anchoring enables a measurement of the bend Frederiks transition, yielding the bend elastic constant of a nematic phase of hard disks as $K_3=7\times {10}^{-14}\text{N}$. By applying a rotating magnetic field on the nematic phase, we observe the bend-splay Frederiks transition, visible as a spatially periodic transient pattern with a wavelength that depends on sample thickness and field strength. Following a linear stability analysis we are able to account for this dependence in a qualitative way. Moreover, the rotating magnetic field enables us to render the nematic phase single domain, with well-defined director orientation.

We report an intrinsic image distortion in microwave-induced thermoacoustic tomography. The distortion, due to microwave diffraction in the object to be imaged, leads to nonuniform excitation of acoustic pressure during microwave illumination. Both numerical simulations and phantom experiments demonstrate this phenomenon. A method of partial correction is also provided.

This paper reports the control of spatiotemporal intermittency in an electroconvective system in a nematic liquid crystal. In the spatiotemporal intermittency, an ordered structure [the defect lattice (DL)] coexists with turbulence. Control of the spatiotemporal intermittency, in which the turbulent state changes to a DL, is achieved by a few percent amplitude modulation of the applied ac voltage. The optimal control frequency is equal to the intrinsic oscillation frequency of the DL. The transition from the turbulent state to a DL occurs not by nucleation of the DL domain, but by penetration of the DL domain into the turbulent one. Control of the spatiotemporal intermittency is achieved through a resonance of the DL oscillation with respect to the modulation frequency that leads to spatial entrainment.

We study intermittent switching behaviors in a system with three identical oscillators coupled diffusively and repulsively, to clarify a bifurcation scenario which generates such intermittent switching behaviors. We use the Stuart-Landau oscillator, which is a general form of Hopf bifurcation, and can describe both cases: limit cycle and inactive (i.e., non-self-oscillatory) cases. From a numerical study of the bifurcation structure, two different routes to chaos which has $S_3$ symmetry were found. One is the sudden appearance of chaos as Pomeau-Manneville intermittency, which is found for the inactive case. In this case a trajectory shows switching among three mutually symmetric tori when a parameter exceeds critical value. The other route, which appears for the limit cycle case, consists of two parts: First, chaos with lower symmetry appears through period doubling, and after the two successive attractor-merging crises, chaos which has $S_3$ symmetry appears. At each crisis, the attractor changes its symmetry.

Computer simulated trajectories of bulk water molecules form complex spatiotemporal structures at the picosecond time scale. This intrinsic complexity, which underlies the formation of molecular structures at longer time scales, has been quantified using a measure of statistical complexity. The method estimates the information contained in the molecular trajectory by detecting and quantifying temporal patterns present in the simulated data (velocity time series). Two types of temporal patterns are found. The first, defined by the short-time correlations corresponding to the velocity autocorrelation decay times $\left(\le 0.1\text{ps}\right)$, remains asymptotically stable for time intervals longer than several tens of nanoseconds. The second is caused by previously unknown longer-time correlations (found at longer than the nanoseconds time scales) leading to a value of statistical complexity that slowly increases with time. A direct measure based on the notion of statistical complexity that describes how the trajectory explores the phase space and independent from the particular molecular signal used as the observed time series is introduced.

We report an experimental result on successfully controlling spiral turbulence in a reaction-diffusion system. The control is realized by periodic forcing in a three-dimensional Belousov-Zhabotinsky reaction-diffusion system, which has chemical concentration gradients in the third dimension. We observe that, in the oscillatory regime of the system, a suitable periodic forcing may stabilize scroll waves (SWs), which otherwise undergo a transition to spiral turbulence. Relating the spiral phase shift due to gradients and the forcing frequency, the mechanism of the control can be well understood by modulating the phase twist of SWs. We use the FitzHugh-Nagumo model to demonstrate this mechanism.

We examine the probability distribution function (PDF) of the energy injection rate (power) in numerical simulations of stationary two-dimensional (2D) turbulence in the Lagrangian frame. The simulation is designed to mimic an electromagnetically driven fluid layer, a well-documented system for generating 2D turbulence in the laboratory. In our simulations, the forcing and velocity fields are close to Gaussian. On the other hand, the measured PDF of injected power is very sharply peaked at zero, suggestive of a singularity there, with tails which are exponential but asymmetric. Large positive fluctuations are more probable than large negative fluctuations. It is this asymmetry of the tails which leads to a net positive mean value for the energy input despite the most probable value being zero. The main features of the power distribution are well described by Craig’s $XY$ distribution for the PDF of the product of two correlated normal variables. We show that the power distribution should exhibit a logarithmic singularity at zero and decay exponentially for large absolute values of the power. We calculate the asymptotic behavior and express the asymmetry of the tails in terms of the correlation coefficient of the force and velocity. We compare the measured PDFs with the theoretical calculations and briefly discuss how the power PDF might change with other forcing mechanisms.

In this paper we analyze the existence, stability, dynamical formation, and mobility properties of localized solutions in a one-dimensional system described by the discrete nonlinear Schrödinger equation with a linear point defect. We consider both attractive and repulsive defects in a focusing lattice. Among our main findings are (a) the destabilization of the on-site mode centered at the defect in the repulsive case, (b) the disappearance of localized modes in the vicinity of the defect due to saddle-node bifurcations for sufficiently strong defects of either type, (c) the decrease of the amplitude formation threshold for attractive and its increase for repulsive defects, and (d) the detailed elucidation as a function of initial speed and defect strength of the different regimes (trapping, trapping and reflection, pure reflection, and pure transmission) of interaction of a moving localized mode with the defect.

The Tsallis entropy and Fisher information entropy (matrix) are very important quantities expressing information measures in nonextensive systems. Stationary and dynamical properties of the information entropies have been investigated in the $N$-unit coupled Langevin model subjected to additive and multiplicative white noise, which is one of typical nonextensive systems. We have made detailed, analytical and numerical study on the dependence of the stationary-state entropies on additive and multiplicative noise, external inputs, couplings, and number of constitutive elements $\left(N\right)$. By solving the Fokker-Planck equation (FPE) by both the proposed analytical scheme and the partial difference equation method, transient responses of the information entropies to an input signal and an external force have been investigated. We have calculated the information entropies also with the use of the probability distribution derived by the maximum-entropy method, whose result is compared to that obtained by the FPE. The Cramér-Rao inequality is shown to be expressed by the extended Fisher entropy, which is different from the generalized Fisher entropy obtained from the generalized Kullback-Leibler divergence in conformity with the Tsallis entropy. The effect of additive and multiplicative colored noise on information entropies is discussed also.

We integrate numerically the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ and $2+1$ dimensions using a Euler discretization scheme and the replacement of ${\left(\nabla h\right)}^2$ by exponentially decreasing functions of that quantity to suppress instabilities. When applied to the equation in $1+1$ dimensions, the method of instability control provides values of scaling amplitudes consistent with exactly known results, in contrast to the deviations generated by the original scheme. In $2+1$ dimensions, we spanned a range of the model parameters where transients with Edwards-Wilkinson or random growth are not observed, in box sizes $8\le L\le 128$. We obtain a roughness exponent of $0.37\le \alpha \le 0.40$ and steady state height distributions with skewness $S=0.25\pm 0.01$ and kurtosis $Q=0.15\pm 0.1$. These estimates are obtained after extrapolations to the large $L$ limit, which is necessary due to significant finite-size effects in the estimates of effective exponents and height distributions. On the other hand, the steady state roughness distributions show weak scaling corrections and evidence of stretched exponential tails. These results confirm previous estimates from lattice models, showing their reliability as representatives of the KPZ class.

In the first part of this series of two papers, we proposed a theoretical formalism that enables one to model and categorize heterogeneous materials (media) via two-point correlation functions $S_2$ and introduced an efficient heterogeneous-medium (re)construction algorithm called the “lattice-point” algorithm. Here we discuss the algorithmic details of the lattice-point procedure and an algorithm modification using surface optimization to further speed up the (re)construction process. The importance of the error tolerance, which indicates to what accuracy the media are (re)constructed, is also emphasized and discussed. We apply the algorithm to generate three-dimensional digitized realizations of a Fontainebleau sandstone and a boron-carbide/aluminum composite from the two-dimensional tomographic images of their slices through the materials. To ascertain whether the information contained in $S_2$ is sufficient to capture the salient structural features, we compute the two-point cluster functions of the media, which are superior signatures of the microstructure because they incorporate topological connectedness information. We also study the reconstruction of a binary laser-speckle pattern in two dimensions, in which the algorithm fails to reproduce the pattern accurately. We conclude that in general reconstructions using $S_2$ only work well for heterogeneous materials with single-scale structures. However, two-point information via $S_2$ is not sufficient to accurately model multiscale random media. Moreover, we construct realizations of hypothetical materials with desired structural characteristics obtained by manipulating their two-point correlation functions.