Using small-angle neutron scattering (SANS), we have investigated the orientational order of iron nanoparticles dispersed in cyclohexanone. The particles have rodlike shape and size distributions with an average length of 200 nm and an average diameter of 25 nm. SANS shows an anisotropy, which is a measure of orientational order, in magnetic dispersions with a volume fraction of 3.2% and 3.9% iron particles in shear flow and/or magnetic field. The scattering anisotropy can be fitted by a model assuming an Onsager distribution of the orientation of the particles in shear flow. The orientational distribution of particles oriented by a magnetic field can be described by a different model assuming the Maier-Saupe orientational distribution for uniaxial ferromagnetic particles. The orientational distribution parameter $m$ for the Maier-Saupe distribution or $\alpha$ for the Onsager distribution and the orientational order parameter $S$ have been determined at shear rates $\dot{\gamma }$ of to $0-4000{\text{s}}^{-1}$ and in magnetic fields of 0–18 mT. The $S$ values indicate that the particles start to orient either in a shear flow of $100{\text{s}}^{-1}$ or in a magnetic field of 6 mT. Applying only shear results in an orientational order, with the dispersion returning to the disordered state when the shear rate is decreased to zero. In sharp contrast, application of magnetic fields greater than 6 mT results in orientational order in the field-increasing cycle, and two-thirds of the orientational order remains when the field is decreased to zero. This shows that the order in a magnetic field is different from the order in a shear flow, the action of magnetizing the particles along a certain direction is irreversible, and the orientational order parameter exhibits hysteresis.

In a phase-separated mixture of two Newtonian polymer solutions sheared in a cone-plate geometry adapted for microscopic observation at a zero-velocity plane, shear-induced coalescence of droplets of the broken-up phase, followed by band formation, was observed. Initially wormlike structures developed into doughnut-shaped bands, disconnected from the walls of the geometry. The shear rate and composition inside the bands differed from that in the outside solution. The shear-shear rate instability preceding the band formation could be qualitatively described by a van der Waals–loop-shaped shear rate dependence of droplet deformation.

In this paper we present the asymptotic solutions of the Poisson-Nernst-Planck equations describing ion transport near a polarized electrode under ac. The solutions can be described in terms of the triple-layer (or quadruple-layer in the transient period) structure. In the thinnest inner layer outside the Stern layer, cations and anions show alternating charging with the same frequency as ac. Next to the inner layer is a buffer region or “middle layer” in which cations and anions exhibit the same behavior but with a frequency double that of the ac frequency. The outer layer shows quasisteady diffusion of ions expanding toward the bulk region and vanishes after the transient period. The potential drop occurs only through the inner layer, which together with the concentrations can be obtained by solving a simple dynamical equation. The asymptotic method is applied to the one-dimensional ion-transport within two parallel facing electrodes and the solutions compare well with the ones obtained with robust numerical methods for the original full equations at various ranges of parameters. We also considered the effect of ion adsorption at the interface between the Stern and inner layers on the ion transport and the virtual slip velocity for the case of facing electrodes.

The competition between reptation and Rouse dynamics is incorporated in the Rubinstein-Duke model for polymer motion by extending it with sideways motions, which cross barriers and create or annihilate hernias. Using the density-matrix renormalization-group method as a solver of the master equation, the renewal time and the diffusion coefficient are calculated as functions of the length of the chain and the strength of the sideways motion. These types of moves have a strong and delicate influence on the asymptotic behavior of long polymers. The effects are analyzed as functions of the chain length in terms of effective exponents and crossover scaling functions.

Dynamic force spectroscopy is a well-established tool to study molecular recognition in a wide range of binding affinities on the single-molecule level. The theoretical interpretation of these data is still very challenging and the models describe the experimental data only partly. In this paper we reconsider the basic assumptions of the models on the basis of an experimental data set and propose an approach of analyzing and quantitatively evaluating dynamic force spectroscopy data on single ligand-receptor complexes. We present our procedure to process and analyze the force-distance curves, to detect the rupture events in an automated manner, and to calculate quantitative parameters for a biophysical characterization of the investigated interaction.

We consider local leaders in random uncorrelated networks, i.e., nodes whose degree is higher than or equal to the degree of all their neighbors. An analytical expression is found for the probability for a node of degree $k$ to be a local leader. This quantity is shown to exhibit a transition from a situation where high-degree nodes are local leaders to a situation where they are not, when the tail of the degree distribution behaves like the power law $\sim k^{-{\gamma }_c}$ with ${\gamma }_c=3$. Theoretical results are verified by computer simulations, and the importance of finite-size effects is discussed.

We study quantum Loschmidt echo, or fidelity, in the triangle map whose classical counterpart has linear instability and weak chaos. Numerically, three regimes of fidelity decay have been found with respect to the perturbation strength $ϵ$. In the regime of weak perturbation, the fidelity decays as $\text{exp}\left(-c{ϵ}^2{t}^{\gamma }\right)$ with $\gamma \simeq 1.7$. In the regime of strong perturbation, the fidelity is approximately a function of $ϵt^{2.5}$, which is predicted for the classical fidelity [G. Casati et al., Phys. Rev. Lett. 94, 114101 (2005)], and decays slower than power-law decay for long times. In an intermediate regime, the fidelity has approximately an exponential decay $\text{exp}\left(-c^{\prime }ϵt\right)$.

We analyze the data stemming from a forced incompressible hydrodynamic simulation on a grid of ${2048}^3$ regularly spaced points, with a Taylor Reynolds number of $R_{\lambda }\sim 1300$. The forcing is given by the Taylor-Green vortex, which shares similarities with the von Kàrmàn flow used in several laboratory experiments; the computation is run for ten turnover times in the turbulent steady state. At this Reynolds number the anisotropic large scale flow pattern, the inertial range, the bottleneck, and the dissipative range are clearly visible, thus providing a good test case for the study of turbulence as it appears in nature. Triadic interactions, the locality of energy fluxes, and longitudinal structure functions of the velocity increments are computed. A comparison with runs at lower Reynolds numbers is performed and shows the emergence of scaling laws for the relative amplitude of local and nonlocal interactions in spectral space. Furthermore, the scaling of the Kolmogorov constant, and of skewness and flatness of velocity increments is consistent with previous experimental results. The accumulation of energy in the small scales associated with the bottleneck seems to occur on a span of wave numbers that is independent of the Reynolds number, possibly ruling out an inertial range explanation for it. Finally, intermittency exponents seem to depart from standard models at high $R_{\lambda }$, leaving the interpretation of intermittency an open problem.

Three-dimensional numerical simulations and direct experimental measurements of the multifilamentation of femtosecond laser pulses propagating in air are quantitatively compared. Agreement is obtained in terms of the evolution of the filamentation pattern and in terms of the size and energy of the individual filaments through $12\mathrm{m}$ of propagation. These results are made possible by the combination of a massively parallel propagation code along with a nondestructive experimental diagnostic technique. Influence of the pulse duration is moreover addressed. The numerical calculations also show that single and multiple filaments exhibit almost identical spectral signature.

Electrostatic charging of powders is a relevant phenomenon for a number of industrial applications. The design of new processes and the use of high resistivity materials and ultrafine powders may lead to higher charging rates and to higher levels of charge accumulation that can become a serious problem. In this work we investigate experimentally electrostatic charging in nanofluidization. The behavior of a fluidized bed of silica nanoparticles under the influence of an electrostatic field is studied. The electric field is applied in the horizontal direction and perpendicular to the gas flow. On one hand, we observe the influence of the electric field on the bulk behavior of the fluidized bed, which suffers a collapse when the electric field is turned on. For strong electric fields the stationary state of the fluidized bed reminds one of that of a spouted bed, with a solid layer adhered to the wall and a low density core region of local high gas velocity. On the other hand, and in order to gain additional insight, we look at the trajectories of nanoparticle agglomerates as affected by the electric field. This images analysis reveals that these agglomerates are horizontally deflected towards the wall as a consequence of being charged. From the analysis of agglomerate trajectories the charge per agglomerate is estimated. Using these measurements the electrostatic forces between agglomerates are calculated and compared to van der Waals attractive forces.

The shapes of shifting sand dunes of different size and under diverse environmental conditions exhibit a remarkably high degree of similarity. On this basis, a reduced shape parametrization of dunes in terms of a few characteristic parameters such as height and length is routinely applied in the geomorphological literature. In view of the a priori extremely high dimensionality of a freely evolving dune’s state space, the justification for this common practice is, despite its alluring simplicity, all but obvious. In order to unveil the origin of the apparent reduction of complexity, we study the dynamics of (slices of) isolated dunes within the framework of the recently proposed minimal model of sand dune formation [K. Kroy, G. Sauermann, and H. J. Herrmann, Phys. Rev. Lett. 88, 054301 (2002); K. Kroy, G. Sauermann, and H. J. Herrmann, Phys. Rev. E 66, 031302 (2002)]. Our numerical solutions—complemented by scaling relations derived from the model equations—show that the predicted time evolution of the shape and size of dunes, in response to naturally varying conditions such as wind strength and sand supply, is subject to a similarity law, closely controlled by the instability modes of the steady-state solutions of the model equations. By this dynamical similarity, the multitude of observed shapes and time evolutions of desert dunes is traced back to a unified growth law and to the elementary scales provided by grain size and wind speed.

The acoustic responses of molecular films with continuous viscoelastic profiles adsorbed on solid-liquid interfaces probed by quartz crystal microbalance (QCM) are analyzed using a continuum mechanics model. The numerically calculated results show that the shift of resonant frequency and the change of dissipation factor of a QCM are determined mostly by the change of viscoelastic profile of the layers in solution adjacent to the quartz-solution interface due to the adsorbed molecular film. For films with the same amount of absorbed mass, the changes in resonant frequency and the dissipation factor vary approximately linearly with the width of the film-solution interface in the profiles. Other viscoelastic properties of the adsorbed films are also affected by the profiles.

The proliferation and migration dichotomy of the tumor cell invasion is examined within a two-component continuous time random walk (CTRW) model. The balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration are derived. The transport of tumor cells is formulated in terms of the CTRW with an arbitrary waiting time distribution law, while proliferation is modeled by a logistic growth. The overall rate of tumor cell invasion for normal diffusion and subdiffusion is determined.

We examine epidemic thresholds for disease spread using susceptible-infected-susceptible models on scale-free networks with variable infectivity. Infectivity between nodes is modeled as a piecewise linear function of the node degree (rather than the less realistic linear transformation considered previously). With this nonlinear infectivity, we derive conditions for the epidemic threshold to be positive. The effects of various immunization schemes including ring and targeted vaccination are studied and compared. We find that both targeted and ring immunization strategies compare favorably to a proportional scheme in terms of effectiveness.

A preformed plasma channel provides a guiding structure for laser pulses unbound by the intensity thresholds of standard waveguides. The recently realized corrugated plasma channel [Layer et al., Phys. Rev. Lett. 99, 035001 (2007)] allows for the guiding of laser pulses with subluminal spatial harmonics. These spatial harmonics can be phase matched to high energy electrons, making the corrugated plasma channel ideal for the acceleration of electrons. We present a simple analytic model of pulse propagation in a corrugated plasma channel and examine the laser-electron beam interaction. Simulations show accelerating gradients of several hundred MeV/cm for laser powers much lower than required by standard laser wakefield schemes.

The gas dynamics of a stationary hot-gas jet supersonically expanding into a low pressure environment is studied through numerical simulations. A hybrid coupled continuum-molecular approach is used to model the flow field. Due to the low pressure and high thermodynamic gradients, continuum mechanics results are doubtful, while, because of its excessive time expenses, a full molecular method is not feasible. The results of the hybrid coupled continuum-molecular approach proposed have been successfully validated against experimental data by R. Engeln et al. [Plasma Sources Sci. Technol. 10, 595 (2001)] obtained by means of laser induced fluorescence. Two main questions are addressed: the necessity of applying a molecular approach where rarefaction effects are present in order to correctly model the flow and the demonstration of an invasion of the supersonic part of the flow by background particles. A comparison between the hybrid method and full continuum simulations demonstrates the inadequacy of the latter, due to the influence of rarefaction effects on both velocity and temperature fields. An analysis of the particle velocity distribution in the expansion-shock region shows clear departure from thermodynamic equilibrium and confirms the invasion of the supersonic part of the flow by background particles. A study made through particles and collisions tracking in the supersonic region further proves the presence of background particles in this region and explains how they cause thermodynamic nonequilibrium by colliding and interacting with the local particles.

The stochastic point processes formed by the zero crossings or extremal points of differentiable, stationary Gaussian processes are studied as a function of their autocorrelation function. The properties of these point processes are mapped to the space formed by the parameters appearing in the autocorrelation function, their adopted form being sensitive to the structure of the autocorrelation function principally in the vicinity of the origin. The distribution for the number of zeros occurring in an asymptotically large interval are approximately negative-binomial or binomial depending upon whether the relative variance or Fano factor is greater or less than unity. The correlation properties of the zeros are such that they are repelled from each other or are “antibunched” if the autocorrelation function of the Gaussian process is characterized by a single scale size, but occur in clusters if more than one characteristic scale size is present. The intervals between zeros can be interpreted in terms of the autocorrelation function of the zeros themselves. When bunching occurs the interval density becomes bimodal, indicating the interval sizes within and between the clusters. The interevent periods are statistically dependent on one another with densities whose asymptotic behavior is governed by that of the autocorrelation function of the Gaussian process at large delay times. Poisson distributed fluctuations of the zeros occur only exceptionally but never form a Poisson process.

We present an approach for the analytical treatment of excitable systems with noise-induced dynamics in the presence of time delay. An excitable system is modeled as a bistable system with a time delay, while another delay enters as a control term taken after Pyragas [K. Pyragas, Phys. Lett. A 170, 421 (1992)] as a difference between the current system state and its state $\tau$ time units before. This approach combines the elements of renewal theory to estimate the essential features of the resulting stochastic process as functions of the parameters of the controlling term.

The present paper introduces a linear reformulation of the Kuramoto model describing a self-synchronizing phase transition in a system of globally coupled oscillators that in general have different characteristic frequencies. The reformulated model provides an alternative coherent framework through which one can analytically tackle synchronization problems that are not amenable to the original Kuramoto analysis. It allows one to solve explicitly for the synchronization order parameter and the critical point of (1) the full phase-locking transition for a system with a finite number of oscillators (unlike the original Kuramoto model, which is solvable implicitly only in the mean-field limit) and (2) a new class of continuum systems. It also makes it possible to probe the system’s dynamics as it moves toward a steady state. While discussion in this paper is restricted to systems with global coupling, the formalism introduced by the linear reformulation also lends itself to solving systems that exhibit local or asymmetric coupling.

We conducted time-dependent, in situ x-ray reflectivity measurements on the formation of substrate-supported lipid monolayers and bilayers at solid-liquid interfaces, buried under an aqueous buffer with various concentrations (5, 10, 20, 40, and $50\mu \text{g}/\text{ml}$) of lipid 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). The DOPC bilayer is formed on the hydrophilic surface of a bare Si substrate, while the DOPC monolayer is formed on a hydrophobic octadecylthricholorsilane (OTS) monolayer-coated Si substrate. The evolution of the reflectivity curves from the lipid bilayers is well described by lateral growth of bilayer islands, consistent with the rupture and fusion model for the adsorption of lipid vesicles to solid-liquid interfaces. By contrast, the formation of the lipid monolayer on OTS-coated Si occurs through a relatively fast coverage of the entire interfacial area, followed by an increase in the monolayer thickness. For both monolayers and bilayers, the rate of lipid layer growth increases with increasing lipid concentration in the buffer solution.