A multicomponent and multiphase model with fluid motion is developed. The model is used to study reactive wetting in the case where concentration change of the spreading liquid and the substrate occurs. With the introduction of a Gibbs energy functional, the governing equations are derived, consisting of convective concentration and phase-field equations which are coupled to the Navier-Stokes equations with surface tension forces. The solid substrate is modeled hydrodynamically with a very high viscosity. Arbitrary phase diagrams, surface energies, and typical dimensionless numbers are some input parameters into the model. An axisymmetric model with an adaptive finite element method is utilized. Numerical simulations were done revealing two stages in the wetting process. First, the convection-dominated stage where rapid spreading occurs. The dynamics of the wetting is found to match with a known hydrodynamic theory for spreading liquids. Second, the diffusion-dominated stage where we observed depression of the substrate-liquid interface and elevation of the contact line region.

The evolution of the domain wall is reduced to the dynamics of the membrane. The rigorous construction of curved membranes in the real scalar field models with domain-wall solutions is presented. An example of the curved membrane is discussed in detail. The curved domain-wall solutions are constructed.

We propose a unifying, analytical theory accounting for the self-organization of colloidal systems in nanocluster or microcluster phases. We predict the distribution of cluster sizes with respect to interaction parameters and colloid concentration. In particular, we anticipate a proportionality regime where the mean cluster size grows proportionally to the concentration, as observed in several experiments. We emphasize the interest in a predictive theory in soft matter, nanotechnologies, and biophysics.

By employing molecular dynamics computer simulations, the phase behavior of systems of rodlike particles with varying degree of internal flexibility has been traced from the perfectly rigid rod limit till very flexible particles, and from the high density region till the isotropic phase. From the perfectly rigid rod limit and enhancing the internal flexibility, the range of the smectic-$\mathit{A}$ phase is squeezed out by the concomitant action of the scarcely affected crystalline phase at higher density and the nematic phase at lower density, until it disappears. These results confirm the supposition, drawn from previous theoretical, simulational and experimental studies, that the smectic-$\mathit{A}$ phase is destabilized by introducing and enhancing the degree of particle internal flexibility. However, no significant changes in the order of nematic–to–smectic-$\mathit{A}$ phase transition, which appears always first order, nor in the value of the layer spacing, are observed upon varying the degree of particle internal flexibility. Moreover, no evidence of a columnar phase, which was thought of as a possible superseder of the smectic-$\mathit{A}$ phase in flexible rods, has been obtained.

The brittle deformation of Arctic sea ice is not only characterized by strong spatial heterogeneity as well as intermittency of stress and strain-rate amplitudes, but also by an intermittency of principal stress directions, with power law statistics of angular fluctuations, long-range correlations in time, and multifractal scaling. This intermittency is much more pronounced than that of wind directions, i.e., is not a direct inheritance of the turbulent forcing.

We propose a method of analysis of dynamical networks based on a recent measure of Granger causality between time series, based on kernel methods. The generalization of kernel-Granger causality to the multivariate case, here presented, shares the following features with the bivariate measures: (i) the nonlinearity of the regression model can be controlled by choosing the kernel function and (ii) the problem of false causalities, arising as the complexity of the model increases, is addressed by a selection strategy of the eigenvectors of a reduced Gram matrix whose range represents the additional features due to the second time series. Moreover, there is no a priori assumption that the network must be a directed acyclic graph. We apply the proposed approach to a network of chaotic maps and to a simulated genetic regulatory network: it is shown that the underlying topology of the network can be reconstructed from time series of node’s dynamics, provided that a sufficient number of samples is available. Considering a linear dynamical network, built by preferential attachment scheme, we show that for limited data use of the bivariate Granger causality is a better choice than methods using $L1$ minimization. Finally we consider real expression data from HeLa cells, 94 genes and 48 time points. The analysis of static correlations between genes reveals two modules corresponding to well-known transcription factors; Granger analysis puts in evidence 19 causal relationships, all involving genes related to tumor development.

We present a perturbation solution for a pressure-driven fluid flow in a rotating toroidal channel. The analysis shows the difference between the solutions of full and simplified equations studied earlier. The result is found to be reliable for low Reynolds number (Re), as was the case for a previously studied solution for high Re. The convergence conditions are defined for the whole range of governing parameters. The viscous flow exhibits some interesting features in flow pattern and hydrodynamic characteristics.

We have studied experimentally and theoretically the response of randomly folded hyperelastic and elastoplastic sheets on the uniaxial compression loading and the statistical properties of crumpling networks. The results of these studies reveal that the mechanical behavior of randomly folded sheets in the one-dimensional stress state is governed by the shape dependence of the crumpling network entropy. Following up on the original ideas by Edwards for granular materials, we derive an explicit force-compression relationship which precisely fits the experimental data for randomly folded matter. Experimental data also indicate that the entropic rigidity modulus scales as the power of the mass density of the folded ball with universal scaling exponent.

The one-dimensional contact process (CP) in a heterogeneous environment—a binary chain consisting of two types of site with different recovery rates—is investigated. It is argued that the commonly used random-sequential Monte Carlo simulation method which employs a discrete notion of time is not faithful to the rates of the contact process in a heterogeneous environment. Therefore, a modification of this algorithm along with two alternative continuous-time implementations are analyzed. The latter two are an adapted version of the $\mathit{n}$-fold way used in Ising model simulations and a method based on a modified priority queue. It is demonstrated that the commonly used (but incorrect as we believe) discrete-time method yields a different critical threshold from all other algorithms considered. Finite-size scaling of the lowest gap in the spectrum of the Liouville time-evolution operator for the CP gives an estimate of the critical rate which supports these findings. Further, a performance test indicates an advantage in using the continuous-time methods in systems with heterogeneous rates. This result promises to help in the analysis of the CP in disordered systems with heterogeneous rates in which simulation is a challenging task due to very long relaxation times.

We present the experimental and numerical study of a method for detecting aperiodic binary signals in a bistable, vertical cavity surface emitting laser (VCSEL). The method uses the phenomenon of vibrational resonance, in presence of a fixed level of noise. We show that the addition of a periodic signal with a period much shorter than the bit duration of the aperiodic input signal allows one to significantly increase the cross-correlation coefficient between the input and the output, as well as to substantially decrease the bit error rate. The experimental observation of a time lag between the input and the output of the VCSEL due the high-frequency modulation is reported. The effect of an asymmetry of the bistable quasipotential on the detection is also analyzed. The numerical results of simulations in a simple model are in qualitative agreement with the experiment.

Fluctuations of the charge $Q_{\Lambda }$ inside a subdomain $\Lambda$ embedded in an electrolyte contained in a finite cubical box of dimensions $L\times L\times L$ with periodic boundary conditions are investigated. When $\Lambda$ is an $L\times L$ “slab” of width $W$, asymptotically exact expressions for the mean-square fluctuation $⟨Q_{\Lambda }^2⟩$ are obtained in terms of the Lebowitz length ${\xi }_{\mathrm{L}}(T,\rho )$ and of the “true” or asymptotic screening/decay length ${\xi }_{Z,\infty }(T,\rho )$ together, when the charge correlation decay is oscillatory, with the characteristic wavelength ${\lambda }_Z(T,\rho )$. In finite systems, the normalized charge fluctuations exhibit threefold scaling behavior in the ratios ${\xi }_{Z,\infty }∕W$, $W∕{\lambda }_Z$, and $W∕L$. This enables one to estimate all the correlation lengths away from criticality quite precisely from finite-size grand canonical Monte Carlo simulations. The results for ${\xi }_{Z,\infty },{\lambda }_Z$, and ${\xi }_{\mathrm{L}}$ are presented for the restricted primitive model or hard-sphere 1:1 electrolyte for densities $\rho \lesssim 1.3{\rho }_c$ and $T\gtrsim 4T_c$. The fitted values compare favorably with the expectations of generalized Debye-Hückel theory [Lee and Fisher, Europhys. Lett. 39, 611 (1997)]; specifically, if ${\xi }_{\mathrm{D}}\propto (T∕\rho {)}^{1∕2}$ is the Debye length, we find ${\xi }_{Z,\infty }<{\xi }_{\mathrm{D}}<{\xi }_{\mathrm{L}}$, although, since ion-pairing is neglected, the charge oscillations set in only for densities $\sim 1.9$ times larger than predicted.

We present a first-principles theory of dynamic arrest in colloidal mixtures based on the multicomponent self-consistent generalized Langevin equation theory of colloid dynamics [M. A. Chávez-Rojo and M. Medina-Noyola, Phys. Rev. E 72, 031107 (2005); M. A. Chávez-Rojo and M. Medina-Noyola, Phys. Rev. E76, 039902 (2007)]. We illustrate its application with a description of dynamic arrest in two simple model colloidal mixtures: namely, hard-sphere and repulsive Yukawa binary mixtures. Our results include observation of the two patterns of dynamic arrest, one in which both species become simultaneously arrested and the other involving the sequential arrest of the two species. The latter case gives rise to mixed states in which one species is arrested while the other species remains mobile. We also derive the (”bifurcation” or fixed-point”) equations for the nonergodic parameters of the system, which takes the surprisingly simple form of a system of coupled equations for the localization length of the particles of each species. The solution of this system of equations indicates unambiguously which species is arrested (finite localization length) and which species remains ergodic (infinite localization length). As a result, we are able to draw the entire ergodic-nonergodic phase diagram of the binary hard-sphere mixture.

Our microscopic stochastic nonlinear Langevin equation theory of activated dynamics has been employed to study the real-space van Hove function of dense hard sphere fluids and suspensions. At very short times, the van Hove function is a narrow Gaussian. At sufficiently high volume fractions, such that the entropic barrier to relaxation is greater than the thermal energy, its functional form evolves with time to include a rapidly decaying component at small displacements and a long-range exponential tail. The “jump” or decay length scale associated with the tail increases with time (or particle root-mean-square displacement) at fixed volume fraction, and with volume fraction at the mean $\alpha$ relaxation time. The jump length at the $\alpha$ relaxation time is predicted to be proportional to a measure of the decoupling of self-diffusion and structural relaxation. At long times corresponding to mean displacements of order a particle diameter, the volume fraction dependence of the decay length disappears. A good superposition of the exponential tail feature based on the jump length as a scaling variable is predicted at high volume fractions. Overall, the theoretical results are in good accord with recent simulations and experiments. The basic aspects of the theory are also compared with a classic jump model and a dynamically facilitated continuous time random-walk model. Decoupling of the time scales of different parts of the relaxation process predicted by the theory is qualitatively similar to facilitated dynamics models based on the concept of persistence and exchange times if the elementary event is assumed to be associated with transport on a length scale significantly smaller than the particle size.

Rippled one-dimensionally periodic structures are commonly seen in the experimental studies of the epitaxial growth and erosion on low symmetry rectangular (110) crystal surfaces. Rippled states period (wavelength) and amplitude grow via a coarsening process that involves motion and annihilations of the dislocations disordering perfect periodicity of these structures. Unlike the ordinary dislocations in equilibrium systems, the dislocations of the growing rippled states are genuinely traveling objects, never at rest. Here, we theoretically elucidate the structure and dynamics of these far-from-equilibrium topological defects. We derive fundamental dislocation dynamics laws that relate the dislocation velocity to the rippled state period. Next, we use our dislocations velocity laws to derive the coarsening laws for the temporal evolution of the rippled state period $\lambda$ and the ripple amplitude $\mathit{w}$ (surface roughness). For the simple rippled states on (110) surfaces, we obtain the coarsening law $\lambda \sim w\sim t^{2/7}$. Under some circumstances however, we find that these states may exhibit a faster coarsening with $\lambda \sim w\sim t^{1/3}$. We also discuss the dislocations in the rectangular rippled surface states for which we derive the coarsening law with $\lambda \sim w\sim t^{1/4}$. The coarsening laws that occur at the transition from the rippled to the rhomboidal pyramid state are also discussed, as well as the crossover effects that occur in rippled states in the proximity of this transition on (110) crystal surfaces.

The statistics of isoheight lines in the $\left(2+1\right)$-dimensional Kardar-Parisi-Zhang (KPZ) model is shown to be conformally invariant and equivalent to those of self-avoiding random walks. This leads to a rich variety of exact analytical results for the KPZ dynamics. We present direct evidence that the isoheight lines can be described by the family of conformally invariant curves called Schramm-Loewner evolution (or ${\text{SLE}}_{\kappa }$) with diffusivity $\kappa =8/3$. It is shown that the absence of the nonlinear term in the KPZ equation will change the diffusivity $\kappa$ from 8/3 to 4, indicating that the isoheight lines of the Edwards-Wilkinson surface are also conformally invariant and belong to the universality class of domain walls in the $O\left(2\right)$ spin model.

We investigate the structure formation in thin films of cylinder forming block copolymers. With in situ scanning probe microscopy image sequences can be recorded with high temporal (2 min per frame) and spatial (10 nm) resolution. We compare different image processing methods for quantitative analysis of the large amount of data. Computing local Minkowski functionals yields local geometrical and morphological information about the observed structures and enables us to track their evolution with time. An alternative characterization method is to reduce the gray scale images to their skeleton and to classify and count the branching points of the skeletonized structure. We tracked the temporal evolution of these measures and computed correlation functions.

We report on a nonmonotonic temperature behavior of the pretilt in cells containing polymers as alignment layers. The latter are very promising since they enable control of the anchoring of the liquid crystal. We show that such a behavior cannot be interpreted by the standard Landau or mean-field theory. We propose a generalization of the mean-field model, including the temperature dependence of the anchoring due to the polymer layer that enables a description of the nonlinear behavior. The agreement between the predictions of the model and the experimental data is good.

Considering the fact that the distances between coupled oscillators may delay the receiving of signals, we study here the influence of uniformly distributed delays in an array of coupled pendulums instead of studying the influence of the coupling strength. We find that with an increase of the range of distributed delays, the chaotic behaviors of the coupled arrays may be controlled and different synchronized patterns can be induced. An analytic solution is given to confirm the numerical results. This finding may provide further insight into information processing in neurons.

The stability of the orientation of scroll rings in the excitable Belousov-Zhabotinsky reaction under an applied electrical current was investigated in experiments and simulations. The parallel and antiparallel orientations of the scroll ring unit vector with respect to the current are two stationary states, the first one unstable, the latter stable. For any other orientation, the scroll rings were forced to rotate by the current. At the stable stationary orientation, the scroll rings may contract or expand under the same applied current depending on the radius of the scroll rings. In simulations, delicate adjustments caused a scroll ring to propagate with a constant radius in an advective field.

We investigate experimentally the statistical properties of active and passive scalar fields in turbulent Rayleigh-Bénard convection in water, at $\text{Ra}\sim {10}^{10}$. Both the local concentration of fluorescence dye and the local temperature are measured near the sidewall of a rectangular cell. It is found that, although they are advected by the same turbulent flow, the two scalars distribute differently. This difference is twofold, i.e., both the quantities themselves and their small-scale increments have different distributions. Our results show that there is a certain buoyant scale based on time domain, i.e., the Bolgiano time scale $t_B$, above which buoyancy effects are significant. Above $t_B$, temperature is active and is found to be more intermittent than concentration, which is passive. This suggests that the active scalar possesses a higher level of intermittency in turbulent thermal convection. It is further found that the mixing of both scalar fields are isotropic for scales larger than $t_B$ even though buoyancy acts on the fluid in the vertical direction. Below $t_B$, temperature is passive and is found to be more anisotropic than concentration. But this higher degree of anisotropy is attributed to the higher diffusivity of temperature over that of concentration. From the simultaneous measurements of temperature and concentration, it is shown that two scalars have similar autocorrelation functions and there is a strong and positive correlation between them.