We discuss the dephasing induced by internal classical chaotic motion in the absence of any external environment. To this end an extension of fidelity for mixed states is introduced, which we name allegiance. Such a quantity directly accounts for quantum interference and is measurable in a Ramsey interferometry experiment. We show that in the semiclassical limit the decay of the allegiance is exactly expressed, due to the dephasing, in terms of an appropriate classical correlation function. Our results are derived analytically for the case of a nonlinear driven oscillator and then numerically confirmed for the kicked rotor model.

The work proposes and studies a model for one-dimensional spatially extended systems, which involve nonlocal interactions and finite propagation speed. It shows that the general reaction-diffusion equation, the Swift-Hohenberg equation, and the general Kuramoto-Sivashinsky equation represent special cases of the proposed model for limited spatial interaction ranges and for infinite propagation speeds. Moreover, the Swift-Hohenberg equation is derived from a general energy functional. After a detailed validity study on the generalization conditions, the three equations are extended to involve finite propagation speeds. Moreover, linear stability studies of the extended equations reveal critical propagation speeds and unusual types of instabilities in all three equations. In addition, an extended diffusion equation is derived and studied in some detail with respect to finite propagation speeds. The extended model allows for the explanation of recent experimental results on non-Fourier heat conduction in nonhomogeneous material.

We propose a way to control solitons in ${\chi }^{\left(2\right)}$ (quadratically nonlinear) systems by means of periodic modulation imposed on the phase-mismatch parameter (“mismatch management,” MM). It may be realized in the cotransmission of fundamental-frequency (FF) and second-harmonic (SH) waves in a planar optical waveguide via a long-period modulation of the usual quasi-phase-matching pattern of ferroelectric domains. In an altogether different physical setting, the MM may also be implemented by dint of the Feshbach resonance in a harmonically modulated magnetic field in a hybrid atomic-molecular Bose-Einstein condensate (BEC), with the atomic and molecular mean fields (MFs) playing the roles of the FF and SH, respectively. Accordingly, the problem is analyzed in two different ways. First, in the optical model, we identify stability regions for spatial solitons in the MM system, in terms of the MM amplitude and period, using the MF equations for spatially inhomogeneous configurations. In particular, an instability enclave is found inside the stability area. The robustness of the solitons is also tested against variation of the shape of the input pulse, and a threshold for the formation of stable solitons is found in terms of the power. Interactions between stable solitons are virtually unaffected by the MM. The second method (parametric approximation), going beyond the MF description, is developed for spatially homogeneous states in the BEC model. It demonstrates that the MF description is valid for large modulation periods, while, at smaller periods, non-MF components acquire gain, which implies destruction of the MF under the action of the high-frequency MM.

A rigorous theory is developed to predict the radiation pressure force (RPF) exerted on a spheroid by an arbitrarily oriented and located shaped beam. Analytical expressions of RPF are derived for a homogeneous spheroid, which can be prolate or oblate, transparent or absorbing. Exemplifying calculations are performed and RPF calculations for spheroids are compared to RPF calculations for spheres. The “Optical Stretcher” is also numerically simulated to study the RPF exerted on a red blood cell during its deformation.

The recent high level of interest in weighted complex networks gives rise to a need to develop new measures and to generalize existing ones to take the weights of links into account. Here we focus on various generalizations of the clustering coefficient, which is one of the central characteristics in the complex network theory. We present a comparative study of the several suggestions introduced in the literature, and point out their advantages and limitations. The concepts are illustrated by simple examples as well as by empirical data of the world trade and weighted coauthorship networks.

Point defects are ubiquitous in two-dimensional crystals and play a fundamental role in determining their mechanical and thermodynamical properties. When crystals are formed on a curved background, finite-length grain boundaries (scars) are generally needed to stabilize the crystal. We provide a continuum elasticity analysis of defect dynamics in curved crystals. By exploiting the fact that any point defect can be obtained as an appropriate combination of disclinations, we provide an analytical determination of the elastic spring constants of dislocations within scars and compare them with existing experimental measurements from optical microscopy. We further show that vacancies and interstitials, which are stable defects in flat crystals, are generally unstable in curved geometries. This observation explains why vacancies or interstitials are never found in equilibrium spherical crystals. We finish with some further implications for experiments and future theoretical work.

The present contribution reports on the observation of two diffusive relaxation modes in a concentrated microemulsion made of repulsive droplets. These two modes can be interpreted in the frame of Weissman’s and Pusey’s theoretical pioneering works. The fast mode is associated to the collective diffusion of droplets whereas the slow one corresponds to the relaxation of droplet concentration fluctuations associated with composition and/or size. We show that (i) repulsive interactions considerably slow down the latter and (ii) a generalized Stokes Einstein relationship between its coefficient of diffusion and the Newtonian viscosity of the solutions, similar to the Walden’s rule for electrolytes, holds for concentrated microemulsion systems made of repulsive droplets.

From positron annihilation lifetime spectroscopy analyzed with the new routine LT9.0 and pressure-volume-temperature experiments analyzed employing the equation of state (EOS) Simha-Somcynsky lattice-hole theory (SS EOS) the microstructure of the free volume and its temperature dependence of an oligomeric epoxy resin (ER6, $M_n\approx 1750\mathrm{g}∕\mathrm{mol}$, $T_g=332\mathrm{K}$) of diglycidyl ether of bisphenol-$A$ (DGEBA) have been examined and characterized by the hole free-volume fraction $h$, the specific free and occupied volumes $V_f=hV$ and $V_{\mathrm{occ}}=(1-h)V$, and the size distribution (mean, $⟨{\nu }_h⟩$, and mean dispersion, ${\sigma }_h$) and the mean density $N_h^{\prime }=V_f∕⟨{\nu }_h⟩$, of subnanometer-size holes. The results are compared with those from a previous work [G. Dlubek et al., Phys. Rev. E 73, 031803 (2006)] on a monomeric liquid of the same resin (ER1, $M_n\approx 380\mathrm{g}∕\mathrm{mol}$, $T_g=255\mathrm{K}$). In the glassy state ER6 shows the same hole sizes as ER1 but a higher $V_f$ and $N_h^{\prime }$. In the liquid $V_f$, $⟨{\nu }_h⟩$, $d{V}_f∕dT$, and $d{V}_f∕dP$ are smaller for ER6. The reported dielectric $\alpha$ relaxation time $\tau$ shows certain deviations from the free-volume model which are larger for ER6 than for ER1. This behavior correlates with the SS EOS, which shows that the unit of the SS lattice is more heavy and bulky and therefore the chain is less flexible for ER6 than for ER1. The free-volume fraction $h$ in the liquid can be described by the Schottky equation $h\propto \exp (-H_h∕k_{B}T)$, where $H_h=7.8$–$6.4\mathrm{kJ}∕\mathrm{mol}$ is the vacancy formation enthalpy, which opens a different way for the extrapolation of the equilibrium part of the free volume. The extrapolated $h$ decreases gradually below $T_g$ and becomes zero only when $0\mathrm{K}$ is reached. This behavior means that no singularity would appear in the relaxation time at temperatures above $0\mathrm{K}$. To quantify the degree to which volume and thermal energy govern the structural dynamics, the ratio of the activation enthalpies $E_i=R\left[\right(d\ln \tau ∕d{T}^{-1}){]}_i$, at constant volume $V$ and constant pressure $P(E_V∕E_P)$, is frequently determined. We present arguments for necessity to substitute $E_V$ by $E_{Vf}$, the activation enthalpy at constant (hole) free volume, and show that $E_{Vf}∕E_P$ changes as expected: it increases with increasing free volume, i.e., with increasing temperature, decreasing pressure, and decreasing molecular weight. $E_{Vf}∕E_P$ exhibits smaller values than $E_V∕E_P$, which leads to the general inference that the free volume plays a larger role in dynamics than concluded from $E_V∕E_P$. The same conclusion is obtained when scaling $\tau$ to $T^{-1}{V}_f^{-\gamma }$ instead of to $T^{-1}{V}^{-\gamma }$, where both $\gamma$’s are material constants.

Fingertip splitting may be observed at chemical reaction fronts subject to buoyancy-induced Rayleigh-Taylor fingering, as investigated in ascending fronts of the iodate-arsenous acid reaction in vertical Hele-Shaw cells. We study the properties of the flow-field evolution during a tip-splitting event both experimentally and theoretically. Experimental particle-image velocimetry techniques show that the flow field associated to a finger displays a quadrupole of vortices. The evolution of the flow field and the reorganization of the vortices after a tip-splitting event are followed experimentally in detail. Numerical integration of a model reaction-diffusion-convection system for an exothermic reaction taking into account possible heat losses through the walls of the reactor shows that the nonlinear properties of the flow field are different whether the walls are insulating or conducting. In insulating systems, the flow field inside one finger features only one pair of vortices. A quadrupole of flow vortices arranged around a saddle-node structure similar to the one observed experimentally is obtained in the presence of heat losses suggesting that heat effects, even if of very small amplitude, are important in understanding the nonlinear properties of fingering of exothermic chemical fronts.

We study the rotation of a weakly conducting particle around its axis of symmetry under the action of the external electric field, which spins in the plane normal to the axis of symmetry of the particle. The particle is embedded in a homogeneous stationary medium with finite electric conductivity permittivity that are different from the corresponding parameters of the particle. We determined the dependence of the particle angular velocity upon the amplitude angular velocity of the electric field. It is shown that depending upon the ratios of the particle electric conductivity permittivity to the corresponding parameters of the host medium the direction of rotation of the particle can be identical or opposite to the direction of rotation of the external electric field. We determined the amplitude-dependent critical angular velocity of the external electric field that separates the domains with two possible regimes of rotation of the particle. In the first domain the particle rotates only in one direction, while in the second domain the particle may rotate in two directions. We investigated also the stability of different regimes of rotation of the particle.

We have characterized a montmorillonite-based organoclay dispersed in three different nonaqueous solvents using a combination of x-ray scattering, small-angle neutron scattering (SANS), and ultrasmall angle neutron scattering (USANS), together with rheological measurements. Consistent with these measurements, we present a structural model for the incompletely dispersed clay as consisting of randomly oriented tactoids made of partially overlapping clay sheets, with transverse dimensions of several microns. Intersheet correlation peaks are visible in x-ray scattering, and quantitatively fit by our model structure factor. SANS and USANS together show a power law of about $-3$ over a wide range of wave numbers below the intersheet correlation peak. Our model relates this power law to a power law distribution of the number of locally overlapping layers in a tactoid. The rheology data show that both storage and loss moduli, as well as yield stress, scale with a power law in volume fraction of about three. Equating the gel onset composition with the overlap of randomly oriented tactoids and taking into account the large transverse dimensions of the tactoids, we predict the gel point to be at or below 0.006 volume fraction organoclay. This is consistent with the rheology data.

In this work, the calcium-induced aggregation of phosphatidylserine liposomes is probed by means of the analysis of the kinetics of such process as well as the aggregate morphology. This novel characterization of liposome aggregation involves the use of static and dynamic light-scattering techniques to obtain kinetic exponents and fractal dimensions. For salt concentrations larger than $5\mathrm{mM}$, a diffusion-limited aggregation regime is observed and the Brownian kernel properly describes the time evolution of the diffusion coefficient. For slow kinetics, a slightly modified multiple contact kernel is required. In any case, a time evolution model based on the numerical resolution of Smoluchowski’s equation is proposed in order to establish a theoretical description for the aggregating system. Such a model provides an alternative procedure to determine the dimerization constant, which might supply valuable information about interaction mechanisms between phospholipid vesicles.

The formation of small nanosized clusters of the proteins holoferritin and apoferritin at low temperature was studied using small angle x-ray scattering. A strikingly large temperature dependence for the average molecular spacing in the clusters was observed. Calculations of the scattered intensity for various cluster models were performed. Comparison of the data with the simulations revealed the presence of crystalline order in the clusters of size ranging from a few molecules to a few hundred molecules. The crystalline order was found to be preserved with the lattice spacing varying with temperature by up to 20%. The small clusters were observed to grow into large micron-sized crystals when they were annealed and under certain conditions, the small clusters were found to coexist with the large crystals. This suggests that these clusters are closely related to critical nucleation. The data are consistent with an isotropic nucleation pathway, but cannot completely rule out a smaller presence of planar nucleation.

We study the dynamics of the spread of an infectious disease within a population partitioned into households, and stratified into resistant and nonresistant individuals. Variability in the level of resistance between households increases the initial rate of spread of the infection, as well as the infection level at the endemic equilibrium. This phenomenon is seen even when all individuals in the population are equally likely to be resistant, and can also be predicted by including spatial clustering of resistant individuals within an improved mean-field approximation.

We derive an exact expression for the magnetization and the zero-field susceptibility of the Ising model on a random graph with degree distribution $P\left(k\right)\propto k^{-\gamma }$ and with a boundary consisting of leaves, that is, vertices whose degree is 1. The system has no magnetization at any finite temperature, and the susceptibility diverges below a certain temperature $T_s$ depending on the exponent $\gamma$. In particular, $T_s$ reaches infinity for $\gamma ⩽4$. These results are completely different from those of the case having no boundary, indicating the nontrivial roles of the leaves in the networks.

A regular array of oscillators with random coupling exhibits a transition from synchronized motion to desynchronized but ordered waves as a global coupling parameter is increased, due to the spread of localized instability of eigenvectors of the Laplacian matrix. We find that shortcuts, which make a regular network small-world, can destroy ordered desynchronization wave patterns. Wave patterns in a small-world network are usually destroyed gradually as the degree of regularity in the network deteriorates. No ordered wave patterns are observed in scale-free and random networks. The formation of ordered wave patterns in a coupled oscillator network can be explained by considering the time evolution of phase in each oscillator. We derive a general type of the Kardar-Parisi-Zhang equation for phase evolution in a prototype oscillator network. The equation demonstrates well the ordered desynchronized wave patterns found in the network with and without shortcuts. Our results provide a qualitative justification for the requirement of certain degree of regularity in the network for ordered wave patterns to arise.

The statistical spectral theory of oscillations in a quasioptical cavity resonator filled with random inhomogeneities is suggested. It is shown that inhomogeneities in the resonator lead to intermode scattering which results in the shift and broadening of spectral lines. The shift and the broadening of each spectral line is strongly depended upon the frequency distance between the nearest-neighbor spectral lines. As this distance increases, the influence of inhomogeneities is sharply reduced. Solitary spectral lines that have quite a large distance to the nearest neighbors are slightly changed due to small inhomogeneities. Owing to such a selective influence of inhomogeneities on spectral lines the effective spectrum rarefaction arises. Both the shift and the broadening of spectral lines as well as spectrum rarefaction in the quasioptical cavity millimeter wave resonator were detected experimentally. We have found out that inhomogeneities result in the resonator spectrum stochastization. As a result, the spectrum becomes composite, i.e., it consists of both regular and random parts. The active self-excited system based on the inhomogeneous quasioptical cavity millimeter wave resonator with a Gunn diode was examined as well. The inhomogeneous quasioptical cavity millimeter wave resonator (passive and active) can serve as a model of a semiconductor quantum billiard. Based on our results we propose that such a billiard with the spectrum rarefied by random inhomogeneities be used as an active semiconductor laser system.

We derive a central limit theorem for the probability distribution of the sum of many critically correlated random variables. The theorem characterizes a variety of different processes sharing the same asymptotic form of anomalous scaling and is based on a correspondence with the Lévy-Gnedenko uncorrelated case. In particular, correlated anomalous diffusion is mapped onto Lévy diffusion. Under suitable assumptions, the nonstandard multiplicative structure used for constructing the characteristic function of the total sum allows us to determine correlations of partial sums exclusively on the basis of the global anomalous scaling.

Efficient tools to characterize stochastic processes are discussed. Quantifiers originally proposed within the framework of information theory, like entropy and statistical complexity, are translated into wavelet language, which renders the above quantifiers into tools that exhibit the important “localization” advantages provided by wavelet theory. Two important and popular stochastic processes, fractional Brownian motion and fractional Gaussian noise, are studied using these wavelet-based informational tools. Exact analytical expressions are obtained for the wavelet probability distribution. Finally, numerical simulations are used to validate our analytical results.

We consider a simple, physically motivated model of a dilute classical gas of interacting particles, initially equilibrated with a heat bath, undergoing adiabatic and quasistatic compression or expansion. This provides an example of a thermodynamic process for which non-Gaussian work fluctuations can be computed exactly from microscopic principles. We find that the work performed during this process is described statistically by a gamma distribution, and we use this result to show that the model satisfies the nonequilibrium work and fluctuation theorems, but not a prediction based on linear response theory.