We investigated nonlinear absorption and photobleaching processes in a liquid-crystal elastomer doped with light-sensitive azobenzene moiety. A conventional one-dimensional holographic grating was recorded in the material with the use of two crossed UV laser beams and the angular dependence of the diffraction efficiency in the vicinity of the Bragg peak was analyzed. These measurements gave information on the depth to which trans to cis isomerization had progressed into the sample as a function of the UV irradiation time. Using a numerical model that takes into account the propagation of writing beams and rate equations for the local concentration of the absorbing trans conformer, we computed the expected spatial distribution of the trans and cis conformers and the shape of the corresponding Bragg diffraction peak for different irradiation doses. Due to residual absorption of the cis conformers the depth of the recording progresses logarithmically with time and is limited by the thermal relaxation from the cis to trans conformation.

By use of optical tweezers we explicitly measure the electrostatic and hydrodynamic forces that determine the electrophoretic mobility of a charged colloidal particle. We test the ansatz of O'Brien and White [J. Chem. Soc. Faraday II 74, 1607 (1978)] that the electrostatically and hydrodynamically coupled electrophoresis problem is separable into two simpler problems: (1) a particle held fixed in an applied electric field with no flow field and (2) a particle held fixed in a flow field with no applied electric field. For a system in the Helmholtz-Smoluchowski and Debye-Hückel regimes, we find that the electrostatic and hydrodynamic forces measured independently accurately predict the electrophoretic mobility within our measurement precision of 7$\%$; the O'Brien and White ansatz holds under the conditions of our experiment.

We present quantitative evidence for x-ray-induced water vaporization: water is vaporized at a rate of 5.5 pL/s with the 1-Å-wavelength x-ray irradiation of ∼0.1 photons per Å${}^2$; moreover, water vapor is reversibly condensed during pauses in irradiation. This result fundamentally suggests that photoionization induces vaporization. This phenomenon is attributed to surface-tension reduction by ionization and would be universally important in radiological and electrohydrodynamic situations.

We consider a chemical reaction network governed by mass action kinetics and composed of $N$ different species which can reversibly form heterodimers. A fast iterative algorithm is introduced to compute te equilibrium concentrations of such networks. We show that the convergence is guaranteed by the Banach fixed point theorem. As a practical example of relevance for a quantitative analysis of microarray data, we consider a reaction network formed by $N\sim {10}^6$ mutually hybridizing different mRNA sequences. We show that, despite the large number of species involved, the convergence to equilibrium is very rapid for most species. The origin of slow convergence for some specific subnetworks is discussed. This provides some insights for improving the performance of the algorithm.

Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a non-Poissonian nature of human behavior on dynamics of opinion formation. We use a variant of the voter model and numerically compare the time to consensus of all the voters with different distributions of interevent intervals and different networks. Compared with the exponential distribution of interevent intervals (i.e., the standard voter model), the power-law distribution of interevent intervals slows down consensus on the ring. This is because of the memory effect; in the power-law case, the expected time until the next update event on a link is large if the link has not had an update event for a long time. On the complete graph, the consensus time in the power-law case is close to that in the exponential case. Regular graphs bridge these two results such that the slowing down of the consensus in the power-law case as compared to the exponential case is less pronounced as the degree increases.

Using Taylor series expansion, multiscaling, and further expansion in powers of a small parameter, we develop general amplitude equations for two-variable reaction-diffusion systems with cross-diffusion terms in the cases of Hopf and Turing instabilities. We apply this analysis to the Oregonator and Brusselator models and find that inhibitor cross diffusion induced by the activator and activator cross diffusion induced by the inhibitor have opposite effects in the two models as a result of the different structure of their community matrices. Our analysis facilitates finding regions of supercritical and subcritical bifurcations, as well as wave and antiwave domains and domains of turbulent waves in the case of Hopf instability.

In the present work, four nontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes system: (i) a stage of the influence of the initial conditions (milliseconds); (ii) one-dimensional (1D) self-similar evolution (milliseconds–seconds); (iii) a primary instability of the self-similar solution (seconds); (iv) a nonlinear stage with secondary instabilities. The self-similar character of evolution at moderately large times is confirmed. Rubinstein and Zaltzman instability and noise-driven nonlinear evolution toward overlimiting regimes in ion-exchange membranes are numerically simulated and compared with theoretical and experimental predictions. The primary instability which happens during this stage is found to arrest a self-similar growth of the diffusion layer. It also specifies its characteristic length as was first experimentally predicted by Yossifon and Chang [G. Yossifon and H.-C. Chang, Phys. Rev. Lett. 101, 254501 (2008)]. A novel principle for the characteristic wave-number selection from the broadband initial noise is established.

We consider wakefield generation in plasmas by electromagnetic pulses propagating perpendicular to a strong magnetic field, in the regime where the electron cyclotron frequency is equal to or larger than the plasma frequency. Particle-in-cell simulations reveal that for moderate magnetic field strengths previous results are reproduced, and the wakefield wave number spectrum has a clear peak at the inverse skin depth. However, when the cyclotron frequency is significantly larger than the plasma frequency, the wakefield spectrum becomes broadband, and simultaneously the loss rate of the driving pulse is much enhanced. A set of equations for the scalar and vector potentials reproducing these results are derived, using only the assumption of a weakly nonlinear interaction.

We study a fractional time derivative generalization of a previous Natale-Salusti model about nonlinear temperature and pressure waves, propagating in fluid-saturated porous rocks. Their analytic solutions, i.e., solitary shock waves characterized by a sharp front, are here generalized, introducing a formalism that allows memory mechanisms. In realistic wave propagation in porous media we must take into account spatial or temporal variability of permeability, diffusivity, and other coefficients due to the system “history.” Such a rock fracturing or fine particulate migration could affect the rock and its pores. We therefore take into account these phenomena by introducing a fractional time derivative to simulate a memory-conserving formalism. We also discuss this generalized model in relation to the theory of dynamic permeability and tortuosity in fluid-saturated porous media. In such a realistic model we obtain exact solutions of Burgers’ equation with time fractional derivatives in the inviscid case.

A group-theoretical approach for studying localized periodic and quasiperiodic vibrations in two- and three-dimensional lattice dynamical models is developed. This approach is demonstrated for the scalar models on the plane square lattice. The symmetry-determined invariant manifolds admitting existence of localized vibrations are found, and some types of discrete breathers are constructed on these manifolds. A general method using the apparatus of matrix representations of symmetry groups to simplify the standard linear stability analysis is discussed. This method allows one to decompose the corresponding system of linear differential equations with time-dependent coefficients into a number of independent subsystems whose dimensions are less than the full dimension of the considered system.

In this paper, we generalize the semiclassical Boltzmann kinetic equation for dilute gases to consider highly nonequilibrium electrons and positrons in soft condensed matter, accounting rigorously for all types of interactions, including positronium formation, and allowing for both coherent and incoherent scattering processes. The limitations inherent in the seminal paper of Cohen and Lekner [M. H. Cohen and J. Lekner, Phys. Rev. 158, 305 (1967); Y. Sakai, J. Phys. D 40, R441 (2007)] are avoided by solving the kinetic equation using a “multiterm” spherical harmonic representation of the velocity distribution function, as well as formulating a necessarily nonperturbative treatment of nonconservative collisional processes such as positronium formation. Numerical calculations of transport properties are carried out for a Percus-Yevick model of a hard-sphere system, and for positrons in liquid argon. New phenomena are predicted, including structure-induced negative conductivity and anisotropic diffusion.

We investigate the long-standing puzzle of phase separation in a granular monolayer vibrated from below. Although this system is three dimensional, an interesting dynamics occurs mostly in the horizontal plane, perpendicular to the direction of vibration. Experiments [Olafsen and Urbach, Phys. Rev. Lett. 81, 4369 (1998)] demonstrated that for a high amplitude of vibration the system is in the gaslike phase, but when the amplitude becomes smaller than a certain threshold, a phase separation occurs: A solidlike dense condensate of particles forms in the center of the system, surrounded by particles in the gaslike phase. We explain theoretically the experimentally observed coexistence of dilute and dense phases, employing Navier-Stokes granular hydrodynamics. We show that the phase separation is associated with a negative compressibility of granular gas.

This paper investigates the combined effects of surface stiffness $\kappa$ and wall particles’ mass $m_w$ on the slip length. It aims to enhance our understanding of the momentum and energy transfer across solid-liquid interfaces. Elastic spring potentials are employed to simulate the thermal solid walls and model the surface stiffness $\kappa$. The thermal oscillation amplitude is primarily dictated by values of stiffness, whereas the oscillating frequency is proportional to $\sqrt{\kappa /m_w}$. It is shown that for cases with variable wall mass the relation of slip length and thermal oscillating frequencies can be approximated by a “master” curve according to which the length initially increases, then approaches a peak value, and afterwards is reduced toward an asymptotic value.

Using the Langevin dynamics simulation, we have studied the effects of shear force on the rupture of short double-stranded DNA at different temperatures. We show that the rupture force increases linearly with chain length and approaches the asymptotic value in accordance with the experiment. The qualitative nature of these curves remains almost the same for different temperatures but with a shift in the force. We observe three different regimes in the extension of covalent bonds (backbone) under shear force.

Emptying a container partially filled with viscous fluid can be a frustratingly slow process. It takes time for the fluid to even begin discharging after tipping the container to develop a draining film on the interior surface. To study the effects of the shape and the tipping angle of the container, we predict the time required for the fluid to begin discharging in two simple geometries. In addition, the volume of the fluid yet to be discharged at subsequent times is predicted to decrease as $t^{-1/2}$ or $t^{-1}$ for flow driven along a plane or corner, respectively. We compare these theoretical predictions with laboratory experiments and discuss how viscous fluids could be poured out most effectively.

We use the cubic complex Ginzburg-Landau equation linearly coupled to a dissipative linear equation as a model for lasers with an external frequency-selective feedback. This system may also serve as a general pattern-formation model in media driven by an intrinsic gain and selective feedback. While, strictly speaking, the approximation of the laser nonlinearity by a cubic term is only valid for small field intensities, it qualitatively reproduces results for dissipative solitons obtained in models with a more complex nonlinearity in the whole parameter region where the solitons exist. The analysis is focused on two-dimensional stripe-shaped and vortex solitons. An analytical expression for the stripe solitons is obtained from the known one-dimensional soliton solution, and its relation with vortex solitons is highlighted. The radius of the vortices increases linearly with their topological charge $m$, therefore the stripe-shaped soliton may be interpreted as the vortex with $m=\infty$, and, conversely, vortex solitons can be realized as unstable stripes bent into stable rings. The results for the vortices are applicable for a broad class of physical systems.

Introduced by Shannon as a “rate of actual transmission,” mutual information rate (MIR) is an extension of mutual information to a pair of dynamical processes. We show a delay-independence theorem, according to which MIR is not sensitive to a time shift between the two processes. Numerical studies of several benchmark situations confirm that this theoretical asymptotic property remains valid for realistic finite sequences. Estimations based on block entropies and a causal state machine algorithm perform better than an estimation based on a Lempel-Ziv compression algorithm provided that block length and maximum history length, respectively, can be chosen larger than the delay. MIR is thus a relevant index for measuring nonlinear correlations between two experimental or simulated sequences when the transmission delay (in input-output devices) or dephasing (in coupled systems) is variable or unknown.

An approach to prognosis of qualitative behavior of an unknown dynamical system (DS) from weakly nonstationary chaotic time series (TS) containing significant measurement noise is proposed. The approach is based on construction of a global time-dependent parametrized model of discrete evolution operator (EO) capable of reproducing nonstationary dynamics of a reconstructed DS. A universal model in the form of artificial neural network (ANN) with certain prior limitations is used for the approximation of the EO in the reconstructed phase space. Probabilistic prognosis of the system behavior is performed using Monte Carlo Markov chain (MCMC) analysis of the posterior Bayesian distribution of the model parameters. The classification of qualitatively different regimes is supposed to be dictated by the application, i.e., it is assumed that some classifier function is predefined that maps a point of a model parameter space to a finite set of different behavior types. The ability of the approach to provide prognosis for times comparable to the observation time interval is demonstrated. Some restrictions as well as possible advances of the proposed approach are discussed.

The ionization-induced scattering of an ultrashort laser pulse is investigated by means of direct modeling of the Maxwell equations. Our results reveal a strongly coupled regime of ionization-induced scattering where structural and temporal characteristics of the laser-matter interactions may change significantly. In this regime, small-scaled plasma inhomogeneities are effectively generated with high plasma densities, even exceeding the critical one.

A method of modifying the roughness of soda-lime glass spheres is presented, with the purpose of tuning interparticle friction. The effect of chemical etching on the surface topography and the bulk frictional properties of grains are systematically investigated. The surface roughness of the grains is measured using white-light interferometry and characterized by the lateral and vertical roughness length scales. The underwater angle of repose is measured to characterize the bulk frictional behavior. We observe that the coefficient of friction depends on the vertical roughness length scale.