To characterize a destruction of Anderson localization by nonlinearity, we study the spreading behavior of initially localized states in disordered, strongly nonlinear lattices. Due to chaotic nonlinear interaction of localized linear or nonlinear modes, energy spreads nearly subdiffusively. Based on a phenomenological description by virtue of a nonlinear diffusion equation, we establish a one-parameter scaling relation between the velocity of spreading and the density, which is confirmed numerically. From this scaling it follows that for very low densities the spreading slows down compared to the pure power law.

In this paper a simple model is proposed for computation of rate coefficients related to vibration-translation transitions based on the forced harmonic oscillator theory. This model, which is developed by considering a quadrature method, provides rate coefficients that are in very good agreement with those found in the literature for the high temperature regime ($\gtrsim 10\hspace{0.5em}000$ K). This model is implemented to study a one-dimensional nonequilibrium inviscid ${\mathrm{N}}_2$ flow behind a plane shock by considering a state-to-state approach. While the effects of ionization and chemical reactions are neglected in our study, our results show that multiquantum transitions have a great influence on the relaxation of the macroscopic parameters of the gas flow behind the shock, especially on vibrational distributions of high levels. All vibrational states are influenced by multiquantum processes, but the effective number of transitions decreases inversely according to the vibrational quantum number. For the initial conditions considered in this study, excited electronic states are found to be weakly populated and can be neglected in modeling. Moreover, the computing time is considerably reduced with the model described in this paper compared to others found in the literature.

Several methods have been developed in the past for analyzing the porosity and other types of well logs for large-scale porous media, such as oil reservoirs, as well as their permeability distributions. We developed a method for analyzing the porosity logs $\varphi (h)$ (where $h$ is the depth) and similar data that are often nonstationary stochastic series. In this method one first generates a new stationary series based on the original data, and then analyzes the resulting series. It is shown that the series based on the successive increments of the log $y(h)=\varphi (h+\delta h)-\varphi (h)$ is a stationary and Markov process, characterized by a Markov length scale $h_M$. The coefficients of the Kramers-Moyal expansion for the conditional probability density function (PDF) $P(y,h|y_0,h_0)$ are then computed. The resulting PDFs satisfy a Fokker-Planck (FP) equation, which is equivalent to a Langevin equation for $y(h)$ that provides probabilistic predictions for the porosity logs. We also show that the Hurst exponent $H$ of the self-affine distributions, which have been used in the past to describe the porosity logs, is directly linked to the drift and diffusion coefficients that we compute for the FP equation. Also computed are the level-crossing probabilities that provide insight into identifying the high or low values of the porosity beyond the depth interval in which the data have been measured.

On certain self-similar substrates the time behavior of a random walk is modulated by logarithmic-periodic oscillations on all time scales. We show that if disorder is introduced in a way that self-similarity holds only in average, the modulating oscillations are washed out but subdiffusion remains as in the perfect self-similar case. Also, if disorder distribution is appropriately chosen the oscillations are localized in a selected time interval. Both the overall random walk exponent and the period of the oscillations are analytically obtained and confirmed by Monte Carlo simulations.

We study the dynamical percolation transition of the geometrical clusters in the two-dimensional Ising model when it is subjected to a pulsed field below the critical temperature. The critical exponents are independent of the temperature and pulse width and are different from the (static) percolation transition associated with the thermal transition. For a different model that belongs to the Ising universality class, the exponents are found to be same, confirming that the behavior is a common feature of the Ising class. These observations, along with a universal critical Binder cumulant value, characterize the dynamical percolation of the Ising universality class.

We propose a nonlinear random walk model which is suitable for the analysis of both chemotaxis and anomalous subdiffusive transport. We derive the master equations for the population density for the case when the transition rate for a random walk depends on residence time, chemotactic substance, and population density. We introduce the anomalous chemotactic sensitivity and find an anomalous aggregation phenomenon. So we suggest a different explanation of the well-known effect of chemotactic collapse.

For radiative heat transfer applications, in particular in homogenized phases of porous media, an exhaustive and accurate validity criterion of the radiative Fourier law, depending only on the logarithmic derivative of the temperature field and an effective absorption coefficient, accounting for possible multiple scattering phenomena, has been established for a semitransparent medium. This effective absorption coefficient is expressed as a function of the absorption coefficient, the albedo, and the scattering asymmetry parameter. The criterion can be applied to semitransparent media that do not follow Beer’s laws related to extinction, absorption, and scattering.

We investigate numerically the spherical shock-wave propagation in an open dense granular packing perturbed by the sudden expansion of a spherical intruder in the interior of the pack, focusing on the correlation between geometrical fabrics and propagating properties. The measurements of the temporal and spatial variations in a variety of propagating properties define a consistent serrated wave substructure with characteristic length on the orders of particle diameters. Further inspection of particle packing reveals a well-defined particle layering that persists several particle diameters away from the intruder, although its dominant effects are only within one to two diameters. This interface-induced layering not only exactly coincides with the serrated wave profile, but also highlights the competition between two energy transmission mechanisms involving distinct transport speeds. The alternating dominances between these two mechanisms contribute to the nonlinear wave propagation on the particle scale. Moreover, the proliferation of intricate three-dimensional contact force networks suggests the anisotropic stress transmission, which is found to also arise from the localized packing structure in the vicinity of the intruder.

The underwater traps of the carnivorous plants of the Utricularia species catch their prey through the repetition of an “active slow deflation followed by passive fast suction” sequence. In this paper, we propose a mechanical model that describes both phases and strongly supports the hypothesis that the trap door acts as a flexible valve that buckles under the combined effects of pressure forces and the mechanical stimulation of trigger hairs, and not as a panel articulated on hinges. This model combines two different approaches, namely (i) the description of thin membranes as triangle meshes with strain and curvature energy, and (ii) the molecular dynamics approach, which consists of computing the time evolution of the position of each vertex of the mesh according to Langevin equations. The only free parameter in the expression of the elastic energy is the Young's modulus $E$ of the membranes. The values for this parameter are unequivocally obtained by requiring that the trap model fires, like real traps, when the pressure difference between the outside and the inside of the trap reaches about 15 kPa. Among other results, our simulations show that, for a pressure difference slightly larger than the critical one, the door buckles, slides on the threshold, and finally swings wide open, in excellent agreement with the sequence observed in high-speed videos.

While communication networks show the small-world property of short paths, the spreading dynamics in them turns out slow. Here, the time evolution of information propagation is followed through communication networks by using empirical data on contact sequences and the susceptible-infected model. Introducing null models where event sequences are appropriately shuffled, we are able to distinguish between the contributions of different impeding effects. The slowing down of spreading is found to be caused mainly by weight-topology correlations and the bursty activity patterns of individuals.

The stress field at the tip of a crack of a thin plate of elastic material that is broken due to a mode III shear tearing has a universal form with a nonuniversal amplitude, known as the stress intensity factor, which depends on the crack length and the boundary conditions. We present in this paper exact analytic results for this stress intensity factor, thus enriching the small number of exact results that can be obtained within linear elastic fracture mechanics.

We investigate a population dynamics model that exhibits a Neimark-Sacker bifurcation with a period that is naturally close to 4. Beyond the bifurcation, the period soon becomes locked at 4 due to a strong resonance, and a second attractor of period 2 emerges, which coexists with the first attractor over a considerable parameter range. A linear stability analysis and a numerical investigation of the second attractor reveal that the bifurcations producing the second attractor occur naturally in this type of system.

Evaporation of water droplets on a superhydrophobic substrate, on which the contact line is pinned, is investigated. While previous studies focused mainly on droplets with contact angles smaller than 90${}^{°}$, here we analyze almost the full range of possible contact angles (10${}^{°}$–150${}^{°}$). The greater contact angles and pinned contact lines can be achieved by use of superhydrophobic carbon nanofiber substrates. The time evolutions of the contact angle and the droplet mass are examined. The experimental data are in good quantitative agreement with the model presented by Popov [Phys. Rev. E 71, 036313 (2005)], demonstrating that the evaporation process is quasistatic, diffusion-driven, and that thermal effects play no role. Furthermore, we show that the experimental data for the evolution of both the contact angle and the droplet mass can be collapsed onto one respective universal curve for all droplet sizes and initial contact angles.

Icicles form when cool water drips from an overhanging support under ambient conditions which are below freezing. Ice growth is controlled by the removal of latent heat, which is transferred into the surrounding air via a thin film of water flowing over the ice surface. We describe laboratory experiments in which icicles were grown under controlled conditions. We used image analysis to probe the evolution of the icicle shape under various conditions. A recent asymptotic theory suggests that, overall, icicles converge to self-similar shapes which are predicted to be attractors. On the other hand, stability theory predicts that the ice-water interface can become unstable to form ripple patterns on the icicle surface. Our experimental results show that the predicted self-similar profile is only found in certain cases, and that icicles can also exhibit unpredicted nonuniformities such as branching near the tip. We find that pure water icicles are more likely to be self-similar than those grown from tap water. Ripples, which are also deviations from the self-similar profile, were observed to climb upward during icicle growth.

The dynamics of the two-dimensional (2D) state in driven three-dimensional (3D) incompressible magnetohydrodynamic turbulence is investigated through high-resolution direct numerical simulations and in the presence of an external magnetic field at various intensities. For such a flow the 2D state (or slow mode) and the 3D modes correspond, respectively, to spectral fluctuations in the plane $k_{\parallel }=0$ and in the area $k_{\parallel }>0$. It is shown that if initially the 2D state is set to zero it becomes nonnegligible in few turnover times, particularly when the external magnetic field is strong. The maintenance of a large-scale driving leads to a break for the energy spectra of 3D modes; when the driving is stopped, the previous break is removed and a decay phase emerges with Alfvénic fluctuations. For a strong external magnetic field the energy at large perpendicular scales lies mainly in the 2D state, and in all situations a pinning effect is observed at small scales.

Exploiting the fractal nature of folded proteins, we study the effect of the hydrodynamic interaction between amino acids using a Zimm-type model. We compute the time-dependent mean square displacement of an amino acid and the time-dependent autocorrelation function of the distance between two amino acids, and we show that these dynamic quantities evolve anomalously, similar to the Rouse-type behavior, yet with modified dynamic exponents. Good agreement is found with recent neutron spin-echo studies of myoglobin and hemoglobin.

The process from a gaseous state to a clustering state for a compartmentalized monodisperse granular gas is accompanied by a drop in the granular temperature to a condensation point. We show experimentally that adding an intruder generally results in a decrease in the condensation point, and a heavier intruder makes this decrease more pronounced. However, once the Brazil nut effect (the intruder on the top of clustering grains) occurs, the condensation point will rise. Through the balance of particle fluxes and the hydrodynamic balance of driving forces, we analytically calculated the condensation point for the monodisperse gases and the intruder-fluid mixtures. The analytical results match the experimental data.

In order to characterize the mechanical behavior of grain piles, we investigate the response of a noncohesive two-dimensional packing of cylinders submitted to a localized force. By means of image processing, we obtain an accurate measurement of the individual grain displacements in the reversible regime of deformation. The measured displacement field deviates unambiguously from the predictions of linear elasticity and of other theoretical descriptions commonly used to model the behavior of cohesionless soils in civil engineering or in soil mechanics. Surprisingly, the analysis of the deformation field reveals a tendency to localization in the reversible regime.

A variety of genome transformations can occur as a microbial population adapts to a large environmental change. In particular, genomic surveys indicate that, following the transition to an obligate, host-dependent symbiont, the density of transposons first rises, then subsequently declines over evolutionary time. Here we show that these observations can be accounted for by a class of generic stochastic models for the evolution of genomes in the presence of continuous selection and gene duplication. The models use a fitness function that allows for partial contributions from multiple gene copies, is an increasing but bounded function of copy number, and is optimal for one fully adapted gene copy. We use Monte Carlo simulation to show that the dynamics result in an initial rise in gene copy number followed by a subsequent falloff due to adaptation to the new environmental parameters. These results are robust for reasonable gene duplication and mutation parameters when adapting to a novel target sequence. Our model provides a generic explanation for the dynamics of microbial transposon density following a large environmental change such as host restriction.

Using Monte Carlo simulations, we deconvolved the sliding and hopping kinetics of GFP-LacI proteins on elongated DNA from their experimentally observed seconds-long diffusion trajectories. Our simulations suggest the following results: (i) in each diffusion trajectory, a protein makes on average hundreds of alternating slides and hops with a mean sliding time of several tens of milliseconds; (ii) sliding dominates the root-mean-square displacement of fast diffusion trajectories, whereas hopping dominates slow ones; (iii) flow and variations in salt concentration have limited effects on hopping kinetics, while in vivo DNA configuration is not expected to influence sliding kinetics; and (iv) the rate of occurrence for hops longer than 200 nm agrees with experimental data for EcoRV proteins.