A harmonic oscillator under the influence of noise is a basic model of various physical phenomena. Under Gaussian white noise the position and velocity of the oscillator are independent random variables which are distributed according to the bivariate Gaussian distribution with elliptic level lines. The distribution of phase is homogeneous. None of these properties hold in the general Lévy case. Thus, the level lines of the joint probability density are not elliptic. The coordinate and the velocity of the oscillator are strongly dependent, and this dependence is quantified by introducing the corresponding parameter (“width deficit”). The distribution of the phase is inhomogeneous and highly nontrivial.

Viscoelastic behaviors in the head-on collisions of polymeric nanodroplets are reported. We propose a new model for normal forces between two colliding droplets. By decomposing the force into an elastic component and a dissipative component and carefully analyzing the equation of motion, we obtain some conditions on the model parameters imposed by the thermodynamic arguments. By employing molecular dynamics simulations, we can explicitly determine the corresponding model parameters by fitting. We compare the model predictions with the simulation results.

We conduct a systematic numerical study of passive scalar structures in supersonic turbulent flows. We find that the degree of intermittency in the scalar structures increases only slightly as the flow changes from transonic to highly supersonic, while the velocity structures become significantly more intermittent. This difference is due to the absence of shocklike discontinuities in the scalar field. The structure functions of the scalar field are well described by the intermittency model of She and Lévêque [Phys. Rev. Lett 72, 336 (1994)], and the most intense scalar structures are found to be sheetlike at all Mach numbers.

An analytical investigation of nonstationary processes in a Duffing oscillator subject to biharmonic forcing, under conditions of primary resonance, is carried out. The earlier developed methodology of limiting phase trajectories (LPTs) for studying highly nonstationary regimes, characterized by intense energy exchanges between the different degrees of freedom, is successfully applied to the system under investigation. Two distinct types of LPT trajectories are described in the first part of the study. Conditions for the recurrent transitions in time from one type of LPT to another were derived in the first part of the analysis corresponding to the undamped case. An approximation of the LPT related to the higher amplitude of oscillations was derived using nonsmooth transformations. An analysis carried out in the study has revealed the necessary and sufficient conditions for excitation of relaxation oscillations exhibited by a lightly damped system. It was also demonstrated that the mechanism of relaxations may be approximated and explained by the methodology of LPTs, characterized by strong energy exchanges between the coupled oscillators or, alternatively, a single oscillator and an external source of energy. The results of analytical approximations and numerical simulations are observed to be in quite satisfactory agreement.

This work presents the results of a detailed experimental study into the transition between synchronized, low-dimensional, and unsynchronized, high-dimensional dynamics using a system of coupled electronic chaotic oscillators. Novel data analysis techniques have been employed to reveal that a hyperchaotic attractor can arise from the amalgamation of two nonattracting sets. These originate from initially multistable low-dimensional attractors which experience a smooth transition from low- to high-dimensional chaotic behavior, losing stability through a bubbling bifurcation. Numerical techniques were also employed to verify and expand on the experimental results, giving evidence on the locally unstable invariant sets contained within the globally stable hyperchaotic attractor. This particular route to hyperchaos also results in the possibility of phenomena (such as unstable dimension variability) that can be a major obstruction to shadowing and predictability in chaotic systems.

One-dimensional systems are under intense investigation, both from theoretical and experimental points of view, since they have rather peculiar characteristics which are of both conceptual and technological interest. We analyze the dependence of the behavior of one-dimensional, time-reversal invariant, nonequilibrium systems on the parameters defining their microscopic dynamics. In particular, we consider chains of identical oscillators interacting via hard-core elastic collisions and harmonic potentials, driven by boundary Nosé-Hoover thermostats. Their behavior mirrors qualitatively that of stochastically driven systems, showing that anomalous properties are typical of physics in one dimension. Chaos, by itself, does not lead to standard behavior, since it does not guarantee local thermodynamic equilibrium. A linear relation is found between density fluctuations and temperature profiles. This link and the temporal asymmetry of fluctuations of the main observables are robust against modifications of thermostat parameters and against perturbations of the dynamics.

A bundle of many fibers with stochastically distributed breaking thresholds is considered as a model of composite materials. The fibers are assumed to share the load equally and to obey Hookean elasticity up to the breaking point. The bundle is slightly overloaded which leads to complete failure. We study the properties of emission bursts in which an amount of energy $E$ is released. The analysis shows that the size of the energy bursts has a minimum when the system is halfway from the collapse point.

We apply the center-of-mass versions of naïve mode coupling theory and nonlinear Langevin equation theory to study how short-range attractive interactions modify the onset of localization, activated single-particle dynamics, and the physical nature of the transiently arrested state of a variety of dense nonspherical particle fluids (and the spherical analog) as a function of volume fraction and attraction strength. The form of the dynamic crossover boundary depends on particle shape, but the reentrant glass-fluid-gel phenomenon and the repulsive glass-to-attractive glass crossover always occur. Diverse functional forms of the dynamic free energy are found for all shapes including glasslike, gel-like, a glass-gel form defined by the coexistence of two localization minima and two activation barriers, and a “mixed” attractive glass characterized by a single, very short localization length but an activation barrier located at a large displacement as in repulsive-force caged glasses. For the latter state, particle trajectories are expected to be of a two-step activated form and can be accessed at high attraction strength by increasing volume fraction, or by increasing attraction strength at fixed high enough volume fraction. A new classification scheme for slow dynamics of fluids of dense attractive particles is proposed based on specification of both the nature of the localized state and the particle displacements required to restore ergodicity via activated barrier hopping. The proposed physical picture appears to be in qualitative agreement with recent computer simulations and colloid experiments.

In paper II of this series we apply the center-of-mass version of Nonlinear Langevin Equation theory to study how short-range attractive interactions influence the elastic shear modulus, transient localization length, activated dynamics, and kinetic arrest of a variety of nonspherical particle dense fluids (and the spherical analog) as a function of volume fraction and attraction strength. The activation barrier (roughly the natural logarithm of the dimensionless relaxation time) is predicted to be a rich function of particle shape, volume fraction, and attraction strength, and the dynamic fragility varies significantly with particle shape. At fixed volume fraction, the barrier grows in a parabolic manner with inverse temperature nondimensionalized by an onset value, analogous to what has been established for thermal glass-forming liquids. Kinetic arrest boundaries lie at significantly higher volume fractions and attraction strengths relative to their dynamic crossover analogs, but their particle shape dependence remains the same. A limited universality of barrier heights is found based on the concept of an effective mean-square confining force. The mean hopping time and self-diffusion constant in the attractive glass region of the nonequilibrium phase diagram is predicted to vary nonmonotonically with attraction strength or inverse temperature, qualitatively consistent with recent computer simulations and colloid experiments.

We quantified the Manning free (uncondensed) counterions fraction $\theta$ for dilute aqueous solutions of rodlike polyions: 150 bp DNA fragments, in the presence of a very low concentration of monovalent salt $c_{\mathrm{salt}}<0.05$ mM. Conductivity measurements of these solutions for DNA base pair concentration range $0.015⩽c⩽8$ mM were complemented by fluorescence correlation spectroscopy (FCS) measurements of the DNA polyion diffusion coefficient $D_p(c)$. We observed a crossover in the normalized conductivity $\sigma (c)/c$ that nearly halved across the $c=0.05$–1 mM range, while $D_p(c)$ remained rather constant, as we established by FCS. Analyzing these data we extracted $\theta (c)=0.30$–0.45, and taking the Manning asymmetry field effect on polyelectrolyte conductivity into account we got $\theta (c)=0.40$–0.60. We relate the $\theta (c)$ variation to gradual DNA denaturation occurring, in the very low salt environment, with the decrease in DNA concentration itself. The extremes of the experimental $\theta (c)$ range occur toward the highest, above 1 mM, and the lowest, below 0.05 mM, DNA concentrations and correspond to the theoretical $\theta$ values for dsDNA and ssDNA, respectively. Therefore, we confirmed Manning condensation and conductivity models to be valuable in description of dilute solutions of rodlike polyions.

We describe and solve a discrete persistent-chain model of protein binding on DNA, involving an extra ${\sigma }_i$ at a site $i$ of the DNA. This variable takes the value 1 or 0, depending on whether or not the site is occupied by a protein. In addition, if the site is occupied by a protein, there is an extra energy cost $\varepsilon$. For a small force, we obtain analytic expressions for the force-extension curve and the fraction of bound protein on the DNA. For higher forces, the model can be solved numerically to obtain force-extension curves and the average fraction of bound proteins as a function of applied force. Our model can be used to analyze experimental force-extension curves of protein binding on DNA, and hence deduce the number of bound proteins in the case of nonspecific binding.

The optimal path crack model on uncorrelated surfaces, recently introduced by Andrade et al. [Phys. Rev. Lett. 103, 225503 (2009).], is studied in detail and its main percolation exponents computed. In addition to $\beta /\nu =0.46\pm 0.03$, we report $\gamma /\nu =1.3\pm 0.2$ and $\tau =2.3\pm 0.2$. The analysis is extended to surfaces with spatial long-range power-law correlations, where nonuniversal fractal dimensions are obtained when the degree of correlation is varied. The model is also considered on a three-dimensional lattice, where the main crack is found to be a surface with a fractal dimension of $2.46\pm 0.05$.

We use semiclassical Hamiltonian optics to investigate the propagation of light rays through two-dimensional photonic crystals when slow spatial modulation of the lattice parameters induces mixed stable-chaotic ray dynamics. This modulation changes both the shape and frequency range of the allowed frequency bands, thereby bending the resulting semiclassical ray trajectories and confining them within particular regions of the crystal. The curved boundaries of these regions, combined with the bending of the orbits themselves, creates a hierarchy of stable and unstable chaotic trajectories in phase space. For certain lattice parameters and electromagnetic wave frequencies, islands of stable orbits act as a dynamical barrier, which separates the chaotic trajectories into two distinct regions of the crystal, thereby preventing the rays propagating through the structure. We show that changing the frequency of the electromagnetic wave strongly affects the distribution of stable and unstable orbits in both real and phase space. This switches the dynamical barriers on and off and thus modulates the transmission of rays through the crystal. We propose microwave analogs of the photonic crystals as a route to the experimental study of the transport effects that we predict.

Detecting chaos and estimating the limit of prediction time in heavy-noise environments is an important and challenging task in many areas of science and engineering. An important first step toward this goal is to reduce noise in the signals. Two major types of methods for reducing noise in chaotic signals are chaos-based approaches and wavelet shrinkage. When noise is strong, chaos-based approaches are not very effective, due to failure to accurately approximate the local chaotic dynamics. Here, we propose a nonlinear adaptive algorithm to recover continuous-time chaotic signals in heavy-noise environments. We show that it is more effective than both chaos-based approaches and wavelet shrinkage. Furthermore, we apply our algorithm to study two important issues in geophysics. One is whether chaos exists in river flow dynamics. The other is the limit of prediction time for the Madden-Julian oscillation (MJO), which is one of the most dominant modes of low-frequency variability in the tropical troposphere and affects a wide range of weather and climate systems. Using the adaptive filter, we show that river flow dynamics can indeed be chaotic. We also show that the MJO is weakly chaotic with the prediction time around 50 days, which is considerably longer than the prediction times determined by other approaches.

The scalar gradient alignment statistics for active and passive scalar gradients (e.g., fuel mass fraction gradient and mixture fraction gradient) are presented here for turbulent stratified flames. It has been shown that, under some conditions, the active scalar gradient may align with the most extensive principal strain rate in contrast to the passive scalar gradient that remains aligned with the most compressive principal strain rate even when the active scalar gradient aligns preferentially with the most extensive principal strain rate. Physical explanations are provided for the observed behaviors.

The possibility of enhancing inner-shell x-ray emission, especially $K\alpha$ emission, by femtosecond-laser irradiation of solid cones instead of foils was investigated theoretically. In a model for hot electron (HE) transport and $K\alpha$ x-ray generation, $K\alpha$ emission from laser-irradiated solid cones and foils is investigated. As a complementarity to the model, the contributions from electric and magnetic fields generated by the HE current in solid cones and foils are discussed. The results indicate that the efficiency of HE energy conversion to $K\alpha$ photons is improved and the optimum HE temperature is increased.

A streamer coupling theory is developed to describe the formation of homogenous emission and the high propagation speed of emission patterns in near-atmospheric pressure discharges. By considering the effects of both electron diffusion and electronic drift in the streamer head, the minimum required preionization level $n_{\min }$ for the formation of streamer coupling is found to be dependent on electric field strength, gas pressure, and electron temperature. The final stage of discharge is a microdischarge, when the preionization level $n_0$ is smaller than $n_{\min }$. However, when $n_0$ is larger than $n_{\min }$, streamers can couple to each other and form a glowlike discharge, and the homogeneity and propagation speed of the emission pattern in the streamer coupling head increases with the preionization level. The streamer coupling model can also be possibly used to explain many phenomenon in near-atmospheric pressure discharges, such as the bulletlike luminous discharge when atmospheric pressure plasma jets eject into ambient air.

The study of microsystems and the development of nanotechnologies require alternative techniques to measure piconewton and femtonewton forces at microscopic and nanoscopic scales. Among the challenges is the need to deal with the ineluctable thermal noise, which, in the typical experimental situation of a spatial diffusion gradient, causes a spurious drift. This leads to a correction term when forces are estimated from drift measurements [G. Volpe, L. Helden, T. Brettschneider, J. Wehr, and C. Bechinger, Phys. Rev. Lett. 104, 170602 (2010)]. Here we provide a systematic study of such an effect by comparing the forces acting on various Brownian particles derived from equilibrium-distribution and drift measurements. We discuss the physical origin of the correction term, its dependence on wall distance and particle radius, and its relation to the convention used to solve the respective stochastic integrals. Such a correction term becomes more significant for smaller particles and is predicted to be on the order of several piconewtons for particles the size of a biomolecule.

The recently demonstrated robustness of fluctuation theorems against measurements [M. Campisi, P. Talkner, and P. Hänggi, Phys. Rev. Lett. 105, 140601 (2010).] does not imply that the probability distributions of nonequilibrium quantities, such as heat and work, remain unaffected. We determine the impact of measurements that are performed during a running force protocol on the characteristic function of work. The results are illustrated by means of the Landau-Zener(-Stückelberg-Majorana) model. In the limit of continuous measurements the quantum Zeno effect suppresses any unitary dynamics. It is demonstrated that the characteristic function of work is the same as for an adiabatic protocol when the continuously measured quantity coincides with the Hamiltonian governing the unitary dynamics of the system in the absence of measurements.

We develop a model to investigate the insulator-conductor transition observed in a system of spherical metal particles suspended in a quasi-two-dimensional viscous liquid between planar electrodes when the voltage of the electrodes is increased. Our model captures the main ingredients of the process in experimental system, and reveals the insulator-conductor transition at a well-defined critical voltage. Based on the simulation data we demonstrate that characteristic quantities of the system show power-law scaling in the vicinity of the critical point. These scaling analysis show clearly that the transition between the insulating and conducting phases is analogous to second-order phase transitions.