The in situ molecular scale response of end-grafted polystyrene to shear against a deuterated polystyrene melt was investigated with neutron reflectometry. The derived grafted polystyrene density profiles showed that the grafted polystyrene was retained on the quartz wafer during the measurements. The profiles suggested that the end-grafted polystyrene response to shear results in a series of metastable states, rather than equilibrium states assumed in the current theory. Except for some possible extension and/or contraction of the grafted polystyrene with shear, there was no obvious correlation between the grafted polymer structure and the shear thinning behavior observed in these samples.

Particles diffusing on a membrane crowded with obstacles have to squeeze between them through funnel-shaped narrow straits. The computation of the mean passage time through the straits is a new narrow escape problem that gives rise to new, hitherto unknown, behavior that we communicate here. The motion through the straits on the coarse scale of the narrow escape time is an effective diffusion with coefficient that varies nonlinearly with the density of obstacles. We calculate the coarse-grained diffusion coefficient on a planar lattice of circular obstacles and use it to estimate the density of obstacles on a neuronal membrane and in a model of a cytoplasm crowded by identical parallel circular rods.

Investigations into molecular motor dynamics are increasingly focused on small-scale features of the motor’s motion. We define performance measures of a common type of single-molecule motility assay, the bead assay, for its ability to detect such features. Using numerical models, we explore the dependence of assay performance on a number of experimentally controllable parameters, including bead size, optical force, and the method of attaching the bead to the motor. We find that the best parameter choice depends on the objective of the experiments, and give a guide to parameter selection. Comparison of the models against experimental data from a recent bead assay of myosin V exemplifies how our methods can also be used to extract additional information from bead assays, particularly that related to small-scale features. By analyzing the experimental data we find evidence for previously undetected multiple waiting states of the bead-motor complex. Furthermore, from numerical simulations we find that equilibrium bead dynamics display features previously attributed to aborted motor steps, and that bead dynamics alone can produce multiple subphases during a step.

We extend a recently proposed model [Chaudhuri et al., Europhys. Lett. 87, 20003 (2009)] aiming to describe the formation of fascicles of axons during neural development. The growing axons are represented as paths of interacting directed random walkers in two spatial dimensions. To mimic turnover of axons, whole paths are removed and new walkers are injected with specified rates. In the simplest version of the model, we use strongly adhesive short-range inter-axon interactions that are identical for all pairs of axons. We generalize the model to adhesive interactions of finite strengths and to multiple types of axons with type-specific interactions. The dynamic steady state is characterized by the position-dependent distribution of fascicle size and fascicle composition. With distance in the direction of axon growth, the mean fascicle size and emergent time scales grow monotonically, while the degree of sorting of fascicles by axon type has a maximum at a finite distance. To understand the emergence of slow time scales, we develop an analytical framework to analyze the interaction between neighboring fascicles.

We present full volumetric (three-dimensional) time-resolved (+one-dimensional) measurements of the velocity field in a large water mixing tank, allowing us to assess spatial and temporal rotational energy (enstrophy) and turbulent energy dissipation intermittency. In agreement with previous studies, highly intermittent behavior is observed, with intense coherent flow structures clustering in the periphery of larger vortices. However, further to previous work the full volumetric measurements allow us to separate out the effects of advection from other effects, elucidating not only their topology but also the evolution of these intense events, through the local balance of stretching and diffusion. These findings contribute toward a better understanding of the intermittency phenomenon, which should pave the way for more accurate models of the small-scale motions based on an understanding of the underlying flow physics.

Epidemics seldom occur as isolated phenomena. Typically, two or more viral agents spread within the same host population and may interact dynamically with each other. We present a general model where two viral agents interact via an immunity mechanism as they propagate simultaneously on two networks connecting the same set of nodes. By exploiting a correspondence between the propagation dynamics and a dynamical process performing progressive network generation, we develop an analytical approach that accurately captures the dynamical interaction between epidemics on overlay networks. The formalism allows for overlay networks with arbitrary joint degree distribution and overlap. To illustrate the versatility of our approach, we consider a hypothetical delayed intervention scenario in which an immunizing agent is disseminated in a host population to hinder the propagation of an undesirable agent (e.g., the spread of preventive information in the context of an emerging infectious disease).

In a recent work [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], Schneider et al. proposed a new measure for network robustness and investigated optimal networks with respect to this quantity. For networks with a power-law degree distribution, the optimized networks have an onion structure—high-degree vertices forming a core with radially decreasing degrees and an over-representation of edges within the same radial layer. In this paper we relate the onion structure to graphs with good expander properties (another characterization of robust network) and argue that networks of skewed degree distributions with large spectral gaps (and thus good expander properties) are typically onion structured. Furthermore, we propose a generative algorithm producing synthetic scale-free networks with onion structure, circumventing the optimization procedure of Schneider et al. We validate the robustness of our generated networks against malicious attacks and random removals.

In this paper we investigate the dynamics of front propagation in the family of reactions $(nA+mB\stackrel{k}{\to }C)$ with initially segregated reactants in one dimension using hyperbolic reaction-diffusion equations with the mean-field approximation for the reaction rate. This leads to different dynamics than those predicted by their parabolic counterpart. Using perturbation techniques, we focus on the initial and intermediate temporal behavior of the center and width of the front and derive the different time scaling exponents. While the solution of the parabolic system yields a short time scaling as $t^{1/2}$ for the front center, width, and global reaction rate, the hyperbolic system exhibits linear scaling for those quantities. Moreover, those scaling laws are shown to be independent of the stoichiometric coefficients $n$ and $m$. The perturbation results are compared with the full numerical solutions of the hyperbolic equations. The crossover time at which the hyperbolic regime crosses over to the parabolic regime is also studied. Conditions for static and moving fronts are also derived and numerically validated.

We investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period January 1996 to July 2009. We discover that the correlation among market indices presents both a fast and a slow dynamics. The slow dynamics reflects the development and consolidation of globalization. The fast dynamics is associated with critical events that originate in a specific country or region of the world and rapidly affect the global system. We provide evidence that the short term time scale of correlation among market indices is less than 3 trading months (about 60 trading days). The average values of the nondiagonal elements of the correlation matrix, correlation-based graphs, and the spectral properties of the largest eigenvalues and eigenvectors of the correlation matrix are carrying information about the fast and slow dynamics of the correlation of market indices. We introduce a measure of mutual information based on link co-occurrence in networks in order to detect the fast dynamics of successive changes of correlation-based graphs in a quantitative way.

We show that intrinsic noise can induce spatiotemporal phenomena such as Turing patterns and traveling waves in a Brusselator model with nonlocal interaction terms. In order to predict and to characterize these stochastic waves we analyze the nonlocal model using a system-size expansion. The resulting theory is used to calculate the power spectra of the stochastic waves analytically and the outcome is tested successfully against simulations. We discuss the possibility that nonlocal models in other areas, such as epidemic spread or social dynamics, may contain similar stochastically induced patterns.

A computational study of the Richtmyer-Meshkov instability for an inclined interface is presented. The study covers experiments to be performed in the Texas A&M University inclined shock tube facility. Incident shock wave Mach numbers from 1.2 to 2.5, inclination angles from 30° to 60°, and gas pair Atwood numbers of ∼0.67 and ∼0.95 are used in this parametric study containing 15 unique combinations of these parameters. Qualitative results are examined through a time series of density plots for multiple combinations of these parameters, and the qualitative effects of each of the parameters are discussed. Pressure, density, and vorticity fields are presented in animations available online to supplement the discussion of the qualitative results. These density plots show the evolution of two main regions in the flow field: a mixing region containing driver and test gas that is dominated by large vortical structures, and a more homogeneous region of unmixed fluid which can separate away from the mixing region in some cases. The interface mixing width is determined for various combinations of the parameters listed at the beginning of the Abstract. A scaling method for the mixing width is proposed using the interface geometry and wave velocities calculated using one-dimensional gas dynamic equations. This model uses the transmitted wave velocity for the characteristic velocity and an initial offset time based on the travel time of strong reflected waves. It is compared to an adapted Richtmyer impulsive model scaling and shown to scale the initial mixing width growth rate more effectively for fixed Atwood number.

Dissipation of mechanical energy underlies the sensitivity of many nanomechanical devices, with environmental effects often having a significant effect. One case of practical relevance is the interaction of elastic beam resonators with fluid, which is known to dramatically increase energy dissipation. Recently, we investigated energy dissipation in a different class of elastic beam resonator that embeds a microfluidic channel in its interior. In this paper, we examine the effect of the beam material Poisson ratio on these devices and discover that it can strongly affect energy dissipation—this is in direct contrast to conventional cantilever beams immersed in fluid. Increasing the Poisson ratio in these microfluidic devices is found to decrease energy dissipation, with the incompressible material limit providing minimum energy dissipation. Our paper establishes that, in this limit, placement of the fluid channel away from the beam neutral axis has negligible effect on energy dissipation in many cases of practical interest. The physical implications of these findings are discussed, and a detailed comparison with available experimental results is provided.

By adjusting the anode current and axial magnetic strength of a dc-glow-discharge dusty plasma, we have found plasma and dust conditions conducive to dusty plasma structurization, similar to the one discussed theoretically by Morfill and Tsytovich [Plasma Phys. Rep. 26, 682 (2000)]. The structurization instability leads to the formation of a pattern where the dust suspension transforms into alternating stationary regions of high and low dust densities. We have measured the dependence of the wavelength of the nonpropagating dust density structures on neutral pressure and plasma density and discussed the results in terms of the dispersion relation obtained by D’Angelo [Phys. Plasmas 5, 3155 (1998)] for an ionization and ion-drag instability. The observations are also considered in light of a recent theoretical prediction by Khrapak et al. [Phys. Rev. Lett. 102, 245004 (2009)] that under certain conditions the effects of the polarization force on dust particles can cause dust acoustic waves to stop propagating, resulting in the formation of aperiodic, stationary dust density structures.

We study experimentally the interaction between two solitary waves that approach one another in a linear chain of spheres interacting via the Hertz potential. When these counterpropagating waves collide, they cross each other and a phase shift in respect to the noninteracting waves is introduced as a result of the nonlinear interaction potential. This observation is well reproduced by our numerical simulations and is shown to be independent of viscoelastic dissipation at the bead contact. In addition, when the collision of equal amplitude and synchronized counterpropagating waves takes place, we observe that two secondary solitary waves emerge from the interacting region. The amplitude of the secondary solitary waves is proportional to the amplitude of incident waves. However, secondary solitary waves are stronger when the collision occurs at the middle contact in chains with an even number of beads. Although numerical simulations correctly predict the existence of these waves, experiments show that their respective amplitudes are significantly larger than predicted. We attribute this discrepancy to the rolling friction at the bead contact during solitary wave propagation.

We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor, coupled together in a periodic ring configuration through inductors and driven uniformly by a harmonic external voltage source. A simple model for each cell is proposed by using a nonlinear form for the varactor characteristics through the current and capacitance dependence on the voltage. For an electrical line composed of 32 elements, we find the regions, in driver voltage and frequency, where $n$-peaked breather solutions exist and characterize their stability. The results are compared to experimental measurements with good quantitative agreement. We also examine the spontaneous formation of $n$-peaked breathers through modulational instability of the homogeneous steady state. The competition between different discrete breathers seeded by the modulational instability eventually leads to stationary $n$-peaked solutions whose precise locations is seen to sensitively depend on the initial conditions.

The concept of soliton management has been explored in the Bose-Einstein condensate and optical fibers. In this paper, our purpose is to investigate whether a similar concept exists for a variable-coefficient modified Korteweg–de Vries equation, which arises in the interfacial waves in two-layer liquid and Alfvén waves in a collisionless plasma. Through the Painlevé test, a generalized integrable form of such an equation has been constructed under the Painlevé constraints of the variable coefficients based on the symbolic computation. By virtue of the Ablowitz-Kaup-Newell-Segur system, a Lax pair with time-dependent nonisospectral flow of the integrable form has been established under the Lax constraints which appear to be more rigid than the Painlevé ones. Under such Lax constraints, multisoliton solutions for the completely integrable variable-coefficient modified Korteweg–de Vries equation have been derived via the Hirota bilinear method. Moreover, results show that the solitons and breathers with desired amplitude and width can be derived via the different choices of the variable coefficients.

We consider here the recently proposed closed-form formula in terms of the Meijer G functions for the probability density functions $g_{\alpha }\left(x\right)$ of one-sided Lévy stable distributions with rational index $\alpha =l/k$, with $0<\alpha <1$. Since one-sided Lévy and Mittag-Leffler distributions are known to be related, this formula could also be useful for calculating the probability density functions ${\rho }_{\alpha }\left(x\right)$ of the latter. We show, however, that the formula is computationally inviable for fractions with large denominators, being unpractical even for some modest values of $l$ and $k$. We present a fast and accurate numerical scheme, based on an early integral representation due to Mikusinski, for the evaluation of $g_{\alpha }\left(x\right)$ and ${\rho }_{\alpha }\left(x\right)$, their cumulative distribution function, and their derivatives for any real index $\alpha \in (0,1)$. As an application, we explore some properties of these probability density functions. In particular, we determine the location and value of their maxima as functions of the index $\alpha$. We show that $\alpha \approx 0.567$ and $0.605$ correspond, respectively, to the one-sided Lévy and Mittag-Leffler distributions with shortest maxima. We close by discussing how our results can elucidate some recently described dynamical behavior of intermittent systems.

We consider the diffusion of Brownian particles in one-dimensional periodic potentials as a test bench for the recently proposed stochastic path integral hyperdynamics (PIHD) scheme [Chen and Horing, J. Chem. Phys. 126, 224103 (2007)]. First, we consider the case where PIHD is used to enhance the transition rate of activated rare events. To this end, we study the diffusion of a single Brownian particle moving in a spatially periodic potential in the high-friction limit at low temperature. We demonstrate that the boost factor as compared to straight molecular dynamics (MD) has nontrivial behavior as a function of the bias force. Instead of growing monotonically with the bias, the boost attains an optimal maximum value due to increased error in the finite path sampling induced by the bias. We also observe that the PIHD method can be sensitive to the choice of numerical integration algorithm. As the second case, we consider parallel resampling of multiple bias force values in the case of a Brownian particle in a periodic potential subject to an external ac driving force. We confirm that there is no stochastic resonance in this system. However, while the PIHD method allows one to obtain data for multiple values of the ac bias, the boost with respect to MD remains modest due to the simplicity of the equation of motion in this case.

As a model of the Brownian motor, we consider a particle moving unidirectionally under the action of two synchronously fluctuating unbiased forces, transverse and longitudinal with respect to the particle track. The former force induces track-normal transitions of the particle between the attached and detached states (with and without a periodic potential, respectively), whereas the latter drives track-parallel motion in either state. Analytical expressions of the current and efficiency are derived for different regimes, with due account of the delayed response of the system to force fluctuations. For a sawtooth potential in the attached state, we reveal several motion regimes affording the maximum current or the maximum efficiency. A special emphasis is placed on the possibility of current reversal. As shown, the interplay between two phase-shifted harmonically varied forces as well as inherent and externally induced asymmetry can lead to the emergence of multiple current reversals, thus enabling the flexible controllability of the motion direction.