A Langmuir film is a molecularly thin film on the surface of a fluid; we study the evolution of a Langmuir film with two coexisting fluid phases driven by an interphase line tension and damped by the viscous drag of the underlying subfluid. Experimentally, we study a $4^{\prime }$-8-alkyl[1,$1^{\prime }$-biphenyl]-4-carbonitrile (8CB) Langmuir film via digitally imaged Brewster angle microscopy in a four-roll mill setup which applies a transient strain and images the response. When a compact domain is stretched by the imposed strain, it first assumes a bola shape with two tear-drop shaped reservoirs connected by a thin tether which then slowly relaxes to a circular domain which minimizes the interfacial energy of the system. We process the digital images of the experiment to extract the domain shapes. We then use one of these shapes as an initial condition for the numerical solution of a boundary-integral model of the underlying hydrodynamics and compare the subsequent images of the experiment to the numerical simulation. The numerical evolutions first verify that our hydrodynamical model can reproduce the observed dynamics. They also allow us to deduce the magnitude of the line tension in the system, often to within 1%. We find line tensions in the range of $200–600\mathrm{pN}$; we hypothesize that this variation is due to differences in the layer depths of the 8CB fluid phases.

A two-site realization of the Davydov model is introduced to study the energy flow between two amide-I modes embedded in a finite size lattice of hydrogen-bounded peptide units. The non-Markovian nature of the energy transfer is addressed by using a time convolutionless master equation for the population difference of quanta between the two sites of the dimer. It is shown that both the lattice size and the dimer position discriminate between two dynamical regimes. For specific values of these parameters, the population difference shows damped oscillations. It decreases exponentially and rapidly vanishes, which indicates that the equilibrium corresponds to a uniform energy distribution over the two sites of the dimer. By contrast, for other specific values of the lattice size and dimer position, a slowdown of the decoherence takes place. The population difference does not decay exponentially but evolves by steps during which the damping of the oscillations is very small. In addition, the occurrence of revivals characterizing an amplification of the coherence over a finite time scale is observed. Nevertheless, both the decoherence slowdown and the revivals are limited by pure dephasing so that the population difference finally vanishes, but after a rather large coherent time.

In this paper we show that both music composition and brain function, as revealed by the electroencephalogram (EEG) analysis, are renewal non-Poisson processes living in the nonergodic dominion. To reach this important conclusion we process the data with the minimum spanning tree method, so as to detect significant events, thereby building a sequence of times, which is the time series to analyze. Then we show that in both cases, EEG and music composition, these significant events are the signature of a non-Poisson renewal process. This conclusion is reached using a technique of statistical analysis recently developed by our group, the aging experiment (AE). First, we find that in both cases the distances between two consecutive events are described by nonexponential histograms, thereby proving the non-Poisson nature of these processes. The corresponding survival probabilities $\Psi \left(t\right)$ are well fitted by stretched exponentials [$\Psi \left(t\right)\propto \exp$ $\mathbf{(}-{\left(\gamma t\right)}^{\alpha }\mathbf{)}$, with $0.5<\alpha <1$.] The second step rests on the adoption of AE, which shows that these are renewal processes. We show that the stretched exponential, due to its renewal character, is the emerging tip of an iceberg, whose underwater part has slow tails with an inverse power law structure with power index $\mu =1+\alpha$. Adopting the AE procedure we find that both EEG and music composition yield $\mu <2$. On the basis of the recently discovered complexity matching effect, according to which a complex system $S$ with ${\mu }_S<2$ responds only to a complex driving signal $P$ with ${\mu }_P⩽{\mu }_S$, we conclude that the results of our analysis may explain the influence of music on the human brain.

A control method for manipulating spatiotemporal chaos is presented using lumped local feedback with several different delay times. As illustrated with the two-dimensional Ginzburg-Landau and the Fitzhugh-Nagumo equation this method can, for example, be used to convert chaotic spiral waves into guided plane waves and for trapping spiral waves.

In this paper, several examples as well as their numerical simulations are provided to show some possible failures of parameter identification based on the so-called adaptive synchronization techniques. These failures might arise not only when the synchronized orbit produced by the driving system is designed to be either some kind of equilibrium or to be some kind of periodic orbit, but also when this orbit is deliberately designed to be chaotic. The reason for emergence of these failures is theoretically analyzed in the paper and the boundedness of all trajectories generated by the coupled systems is rigorously proved. Moreover, synchronization techniques are proposed to realize complete synchronization and unknown parameter identification in a class of systems where nonlinear terms are not globally Lipschitz. In addition, unknown parameter identification is studied in coupled systems with time delays.

In the present work, we study dark solitons in dynamical lattices with the saturable nonlinearity and compare them to those in lattices with the cubic nonlinearity. This comparison has become especially relevant in light of recent experimental developments in the former context. The stability properties of the fundamental waves, for both onsite and intersite modes, are examined analytically and corroborated by numerical results. Our findings indicate that for both models onsite solutions are stable for sufficiently small values of the coupling between adjacent nodes, while intersite solutions are always unstable. The nature of the instability (which is oscillatory for onsite solutions at large coupling and exponential for inter-site solutions) is probed via the dynamical evolution of unstable solitary waves through appropriately crafted numerical experiments; typically, these computations result in dynamic motion of the originally stationary solitary waves. Another key finding, consistent with recent experimental results, is that the instability growth rate for the saturable nonlinearity is found to be smaller than that of the cubic case.

We present a solution to the problem of partial reflection and refraction of a polarized paraxial Gaussian beam at the interface between two transparent media. The Fedorov-Imbert transverse shifts of the centers of gravity of the reflected and refracted beams are calculated. Our results differ in the general case from those derived previously by other authors. In particular, they obey general conservation law for the beams’ total angular momentum but do not obey one-particle conservation laws for individual photons, which have been proposed by [Onoda et al. Phys. Rev. Lett. 93, 083901 (2004)]. We ascertain that these circumstances relate to the artificial model accepted in the literature for the polarized beam; this model does not fit to real beams. The present paper resolves the recent controversy and confirms the results of our previous paper [Bliokh et al. Phys. Rev. Lett. 96, 073903 (2006)]. In addition, a diffraction effect of angular transverse shifts of the reflected and refracted beams is described.

We describe the onset of spatiotemporal chaos in a spatially extended nonlinear dynamical system as a result of the loss of transversal stability of an invariant manifold representing a spatially homogeneous and temporally chaotic state. The onset of spatiotemporal chaos is characterized by the switching between spatially homogeneous and nonhomogeneous states with statistical properties of on-off intermittency.

We present a model for predicting the spatial intensity correlation function of dynamic speckle patterns formed by light backscattered from turbid suspensions, and an experimental validation of these predictions. The spatial correlation varies remarkably with multiple scattering. The provided computational scheme is a step towards correctly interpreting signals obtained from instruments based on the measurement of dynamic speckle patterns in the far field.

A simple theory for the leading-order correction $g_1\left(r\right)$ to the structure of a hard-sphere liquid with discrete (e.g., square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively eliminates four-particle correlations from $g_1\left(r\right)$ with good accuracy at high densities. For the particular case of discrete perturbations, the remaining three-particle correlations can be modeled with a simple volume-exclusion argument, resulting in an algebraic and surprisingly accurate expression for $g_1\left(r\right)$. The structure of a discrete “core-softened” model for liquids with anomalous thermodynamic properties is reproduced as an application.

The experimental work presented focuses on transient growth, morphological transitions, and control of xenon dendrites. Dendritic free growth is perturbed by two different mechanisms: Shaking and heating up to the melting temperature. Spontaneous and metastable multitip configurations are stabilized, coarsening is reduced, leading to a denser sidebranch growth, and a periodic tip splitting is found during perturbation by shaking. On the other hand, heating leads to controlled sidebranching and characteristic transitions of the tip shape. A deterministic behavior is found besides the random-noise-driven growth. The existence of a limit cycle is supported by the findings. Together the two perturbation mechanisms allow a “dendrite engineering”—i.e., a reproducible controlling of the crystal shape during its growth. The tip splitting for dendritic free growth is found not to be a splitting of the tip in two; rather, the respective growth velocities of the main tip and the fins change. The latter then surpass the main tip and develop into new tips. The occurrence of three- and four-tip configurations is explained with this mechanism. Finite-element calculations of the heat flow and the convective flow in the growth vessel show that the idea of a single axisymmetric toroidal convection roll across the whole growth vessel has to be dropped. The main effect of convection under Earth’s gravity is the compression of the diffusive temperature field around the downward-growing tip. A model to explain the symmetry of dendritic crystals—e.g., snow crystals—is developed, based on the interaction of crystal shape and heat flow in the crystal.

Spatiotemporal chaos on a regular ring network of excitable Gray-Scott dynamical elements collapses to a stable asymptotic state. We find that the addition of dynamical noise clearly influences the spatiotemporal pattern and the transient lifetime of spatiotemporal chaos. Spatially uniform noise significantly decreases the average lifetime of spatiotemporal chaos due to an enlargement of regions of local collapse. For spatially inhomogeneous noise the collapse is maximally delayed at an intermediate noise level, but drastically advanced for larger noise levels.

Electric-field-driven pattern formation has been investigated in a nematic liquid crystal with negative dielectric and conductivity anisotropies. Despite the fact that the standard Carr-Helfrich theory predicts no hydrodynamic instability for such compound, experiments reveal convection patterns which we call nonstandard electroconvection (ns-EC). In this work, we characterize the ns-EC patterns by measuring the frequency, thickness, and temperature dependence of the threshold voltage, wave number, roll orientation, etc., and compare them with the standard-EC (s-EC) characteristics. For the first time, we report traveling rolls in ns-EC, and we give the dependence of the Hopf frequency on the driving frequency, temperature, and sample thickness. Finally, we discuss possible sources for the existence of these patterns.

Based on an automatic feedback adjustment of an additional parameter of a dynamical system, we propose a strategy for controlling periodic orbits of desired periods in chaotic dynamics and tracking them toward the set of unstable periodic orbits embedded within the original chaotic attractor. The method does not require information on the system to be controlled, nor on any reference states for the targets, and it overcomes some of the difficulties encountered by other techniques. Assessments of the method’s effectiveness and robustness are given by means of the application of the technique to the stabilization of unstable periodic orbits in both discrete- and continuous-time systems.

We derive an exact expression for entropy production during effusion of an ideal gas driven by momentum transfer in addition to energy and particle flux. Following the treatment in Cleuren et al. [Phys. Rev. E 74, 021117 (2006)], we construct a master equation formulation of the process and explicitly verify the thermodynamic fluctuation theorem, thereby directly exhibiting its extended applicability to particle flows and hence to hydrodynamic systems.

Consider $N$ points randomly distributed along a line segment of unitary length. A walker explores this disordered medium, moving according to a partially self-avoiding deterministic walk. The walker, with memory $\mu$, leaves from the leftmost point and moves, at each discrete time step, to the nearest point that has not been visited in the preceding $\mu$ steps. Using open boundary conditions, we have calculated analytically the probability $P_N\left(\mu \right)=(1-2^{-\mu }{)}^{N-\mu -1}$ that all $N$ points are visited, with $N\gg \mu \gg 1$. This approximated expression for $P_N\left(\mu \right)$ is reasonable even for small $N$ and $\mu$ values, as validated by Monte Carlo simulations. We show the existence of a critical memory ${\mu }_1=\ln N∕\ln 2$. For $\mu <{\mu }_1-e∕\left(2\ln 2\right)$, the walker gets trapped in cycles and does not fully explore the system. For $\mu >{\mu }_1+e∕\left(2\ln 2\right)$, the walker explores the whole system. Since the intermediate region increases as $\ln N$ and its width is constant, a sharp transition is obtained for one-dimensional large systems. This means that the walker need not have full memory of its trajectory to explore the whole system. Instead, it suffices to have memory of order ${\log }_{2}N$.

A scaling law for the $\alpha$ relaxation time $\tau$, involving the ratio of a density-dependent energy to the thermal energy, has been found to hold in many fragile glass-forming liquids. This scaling has been recently linked to a local quantity $n_{loc}(\rho ,T)$ relating the variation of $\tau$ with density to its variation with temperature. In many fragile liquids, the variation of $n_{loc}(\rho ,T)$ is weak enough to take it as constant over the experimental temperature and density domain. We show that simulated liquid silica has an opposite behavior; close to $T_g$, $n_{loc}$ is negative for moderate densities and exhibits a significant variation with $\rho$ and $T$, reaching positive values for higher temperature and/or densities. Moreover, those variations linearly correlate to a measure of the bonding properties of the liquid.

An equation describing the evolution of phenotypic distribution is derived using methods developed in statistical physics. The equation is solved by using the singular perturbation method, and assuming that the number of bases in the genetic sequence is large. Applying the equation to the mutation-selection model by Eigen provides the critical mutation rate for the error catastrophe. Phenotypic fluctuation of clones (individuals sharing the same gene) is introduced into this evolution equation. With this formalism, it is found that the critical mutation rate is sometimes increased by the phenotypic fluctuations, i.e., noise can enhance robustness of a fitted state to mutation. Our formalism is systematic and general, while approximations to derive more tractable evolution equations are also discussed.

The motion of an ensemble of particles in a space-periodic potential well with a weak wavelike perturbation imposed is considered. We found that slow oscillations of the wave number of the perturbation lead to the occurrence of directed particle current. This current is amplified with time due to the giant acceleration of some particles. It is shown that giant acceleration is linked to the existence of resonant channels in phase space.

We study persistence in coupled circle maps with repulsive (inhibitory) coupling, and find that it offers an effective way to characterize the synchronous, traveling wave and spatiotemporally chaotic states of the system. In the traveling wave state, persistence decays as a power law and, in contrast to earlier observations in dynamical systems, this power-law scaling does not occur at the transition point alone, but over the entire dynamical phase (with the same exponent). We give a cellular automata model displaying the qualitative features of the traveling wave regime and provide an argument based on the theory of Motzkin numbers in combinatorics to explain the observed scaling.