We here develop a theory for the effect of shearing flow on residual proton dipole-dipole interactions for polymer melts. The model is based on the use of correlation functions which derive from the return to origin probability for polymers reptating in the tube of surrounding constraints. Using Doi-Edwards theory we calculate the spin-echo response under equilibrium conditions and then consider the effect of a shearing flow which deforms the tube, finding that there exists a strong dependence of transverse relaxation on Weissenberg number. The results are compared with NMR measurements of shear-perturbed proton $T_2$ relaxation in $494\mathrm{kDa}$ poly (dimethylsiloxane).

We report on the nonlinear mechanical properties of a statistically homogeneous, isotropic semiflexible network cross-linked by polymers containing numerous small unfolding domains, such as the ubiquitous F-actin cross-linker filamin. We show that the inclusion of such proteins has a dramatic effect on the large strain behavior of the network. Beyond a strain threshold, which depends on network density, the unfolding of protein domains leads to bulk shear softening. Past this critical strain, the network spontaneously organizes itself so that an appreciable fraction of the filamin cross-linkers are at the threshold of domain unfolding. We discuss via a simple mean-field model the cause of this network organization and suggest that it may be the source of power-law relaxation observed in in vitro and in intracellular microrheology experiments. We present data which fully justify our model for a simplified network architecture.

We study the influence of the structural diversity of cells on subthreshold agonist signals in coupled hepatocytes systems. The variance of the cellular structural parameter $\sigma$ is employed to characterize the structural diversity. It is found that structural diversity enhances the cellular ability to detect extracellular weak signals through intracellular ${\mathrm{Ca}}^{2+}$ oscillations and the regularity of ${\mathrm{Ca}}^{2+}$ spikes undergoes a maximum with a variation of $\sigma$, indicating the occurrence of structural-diversity-induced coherence resonance. Furthermore, the effects of the level of subthreshold stimulus and junctional coupling strength on the behavior of ${\mathrm{Ca}}^{2+}$ dynamics are also considered. Analysis indicates that these phenomena have inherent relevance to both the bifurcation feature of a single cell and intercellular interaction through junctional coupling. Our findings may exhibit that structural diversity plays a constructive role in biological systems.

We propose a three-species ($A$, $B$, and $C$) exchange-driven aggregate growth model with competition between catalyzed birth and catalyzed death. In the system, exchange-driven aggregation occurs between any two aggregates of the same species with the size-dependent rate kernel $K_n(k,j)=K_{n}kj$ $(n=1,2,3)$, and, meanwhile, monomer birth and death of species $A$ occur under the catalysis of species $B$ and $C$ with the catalyzed birth and catalyzed death rate kernels $I(k,j)=Ik{j}^v$ and $J(k,j)=Jk{j}^v$, respectively. The kinetic behavior is investigated by means of the mean-field rate equation approach. The form of the aggregate size distribution $a_k\left(t\right)$ of species $A$ is found to depend crucially on the competition between species-$B$-catalyzed birth of species $A$ and species-$C$-catalyzed death of species $A$, as well as the exchange-driven growth. The results show that (i) when exchange-driven aggregation dominates the process, $a_k\left(t\right)$ satisfies the conventional scaling form; (ii) when catalyzed birth dominates the process, $a_k\left(t\right)$ takes the conventional or generalized scaling form; and (iii) when catalyzed death dominates the process, the aggregate size distribution of species $A$ evolves only according to some modified scaling forms.

The effect of a time-periodic chaotic shear flow on an excitable chemical medium is studied numerically. Stirring effects on pattern formation strongly depend on the shear amplitude and the ratio of the advective and chemical time scales (Damköhler number, Da). We have observed that the wave period increases with decreasing Da below some critical value, afterwards the period decreases until complete wave annihilation. In the last case, before final extinction, a set of uncorrelated, nonstationary excitable dots survive, whose number depends on the mixing rate. Insights on the nature of this critical behavior are obtained through the calculation of the mixing efficiency of the flow.

The link between phase coherence and non-Gaussian statistics is investigated using magnetic field data observed in the solar wind turbulence near the Earth’s bow shock. The phase coherence index $C_{\varphi }$, which characterizes the degree of phase correlation (i.e., nonlinear wave-wave interactions) among scales, displays a behavior similar to kurtosis and reflects a departure from Gaussianity in the probability density functions of magnetic field fluctuations. This demonstrates that nonlinear interactions among scales are the origin of intermittency in the magnetic field turbulence.

We consider the magnetorotational instability (MRI) of a hydrodynamically stable Taylor-Couette flow with a helical external magnetic field in the inductionless approximation defined by a zero magnetic Prandtl number $(\mathrm{Pm}=0)$. This leads to a considerable simplification of the problem eventually containing only hydrodynamic variables. First, we point out that magnetic field adds more dissipation while it does not change the base flow which is the only source of energy for growing perturbations. Thus, it seems unclear from the energetic point of view how such a hydrodynamically stable flow can turn unstable in the presence of a helical magnetic field as it has been found recently by Hollerbach and Rüdiger [Phys. Rev. Lett. 95, 124501 (2005)]. We revisit this problem by using a Chebyshev collocation method to calculate the eigenvalue spectrum of the linearized problem. In this way, we confirm that a helical magnetic field can indeed destabilize the flow in the inductionless approximation. Second, we integrate the linearized equations in time to study the transient behavior of small amplitude perturbations, thus showing that the energy arguments are correct as well. However, there is no real contradiction between both facts. The linear stability theory predicts the asymptotic development of an arbitrary small-amplitude perturbation, while the energy stability theory yields the instant growth rate of any particular perturbation, but it does not account for the evolution of this perturbation. Thus, although switching on the magnetic field instantly increases the energy decay rate of the dominating hydrodynamic perturbation, in the same time this perturbation ceases to be an eigenmode in the presence of the magnetic field. Consequently, this perturbation is transformed with time and so becomes able to extract energy from the base flow necessary for the growth.

We show that two-dimensional bidisperse assemblies of colloids with strictly repulsive interactions exhibit stripe, cluster, and partially crystallized states when driven over a quenched random substrate. The nonequilibrium states on a substrate are significantly more ordered than equilibrium states both with and without substrates. A minimum substrate strength is necessary to induce the nonequilibrium pattern formation. Our results suggest that a combination of driving and quenched disorder offers a new approach to controlling pattern formation in colloid mixtures.

We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of globally connected arrays of $\mathcal{N}$ types of oscillators $(\mathcal{N}=2,3,4)$ by exploring the linear stability of the nonsynchronous fixed point. We also provide results for globally coupled arrays where the transition rate of each unit is drawn from a uniform distribution of finite width. Even in the presence of transition rate disorder, numerical and analytical results point to a single phase transition to macroscopic synchrony at a critical value of the coupling strength. Numerical simulations make possible further characterization of the synchronized arrays.

The translational motion of a solid sphere near a deformable fluid interface is studied in the low Reynolds number regime. In this problem, the fluid flow driven by the sphere is dynamically coupled to the instantaneous conformation of the interface. Using a two-dimensional Fourier transform technique, we are able to account for the multiple backflows scattered from the interface. The correction to the mobility tensor is then obtained from the matrix elements of the relevant Green’s function. Our perturbative analysis allows us to express the explicit position and frequency dependence of the mobility for small particles. We recover in the steady limit the result for a sphere near a perfectly flat interface. At intermediate time scales, the mobility exhibits an imaginary part which is a signature of the elastic response of the interface. In the short time limit, we find that the perpendicular mobility may, under some circumstances, become lower than the bulk value. All the results can be explained using the definition of the relaxation time of the soft interface.

We apply percolation theory to a recently proposed measure of fragmentation $F$ for social networks. The measure $F$ is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after removing a fraction $q$ of nodes and the total number of pairs in the original fully connected network. We compare $F$ with the traditional measure used in percolation theory, $P_{\infty }$, the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods from percolation, we study Erdős-Rényi and scale-free networks under various types of node removal strategies. The removal strategies are random removal, high degree removal, and high betweenness centrality removal. We find that for a network obtained after removal (all strategies) of a fraction $q$ of nodes above percolation threshold, $P_{\infty }\approx {(1-F)}^{1∕2}$. For fixed $P_{\infty }$ and close to percolation threshold $(q=q_c)$, we show that $1-F$ better reflects the actual fragmentation. Close to $q_c$, for a given $P_{\infty }$, $1-F$ has a broad distribution and it is thus possible to improve the fragmentation of the network. We also study and compare the fragmentation measure $F$ and the percolation measure $P_{\infty }$ for a real social network of workplaces linked by the households of the employees and find similar results.

The shear-current effect in a nonrotating homogeneous turbulent convection with a large-scale constant shear is studied. The large-scale velocity shear causes anisotropy of turbulent convection, which produces the mean electromotive force ${\mathcal{E}}^{\left(W\right)}\propto \mathbf{W}\times \mathbf{J}$ and the mean electric current along the original mean magnetic field, where $\mathbf{W}$ is the background mean vorticity due to the shear and $\mathbf{J}$ is the mean electric current. This results in a large-scale dynamo even in a nonrotating and nonhelical homogeneous sheared turbulent convection, whereby the $\alpha$ effect vanishes. It is found that turbulent convection promotes the shear-current dynamo instability, i.e., the heat flux causes positive contribution to the shear-current effect. However, there is no dynamo action due to the shear-current effect for small hydrodynamic and magnetic Reynolds numbers even in a turbulent convection, if the spatial scaling for the turbulent correlation time is $\tau \left(k\right)\propto k^{-2}$, where $k$ is the small-scale wave number.

An experimental technique for measuring time-resolved coherence loss and destruction of backscattered wave packets in random media is described. The results of such measurements, performed with a modified Michelson interferometer, contain rich information about the characteristics of media nonuniformities. Experimental data for model nanosuspensions are compared with theoretical expressions developed in the paper which include the effects of Mie-type resonant scattering. We attribute one such observed effect to enhanced ineleastic optical transitions near the surface of nonmetallic nanoparticles. The inverse problem of characterization of multiscattering random media by backscattering is also considered.

By analogy with the electromagnetic wave, the acoustic transparency phenomenon is analyzed for a multilayered sphere with acoustic metamaterials. The neutral-inclusion concept is used to predict the transparency conditions in the quasistatic case, which are further confirmed by a full-wave analysis. The mechanism of the transparency is based on lowering the total-scattering cross section of the composite sphere. It is found that, to improve the transparency, the angle-dependent scattering cross section must also be minimized for all directions.

We present a method to calculate Lyapunov exponents of rigid diatomic molecules in three dimensions ($12N$-dimensional phase space). The spectra of Lyapunov exponents are obtained for 32 rigid diatomic molecules interacting through the Weeks-Chandler-Anderson potential for various bond length and densities, and compared with those of Shin et al. [Phys. Rev. E 64, 041106 (2001)]. Our algorithm is easy to implement and total CPU time is relatively inexpensive.

With Monte Carlo methods, we simulate dynamic relaxation processes of the two-dimensional $XY$ model at the Berezinskii-Kosterlitz-Thouless phase transition temperature and below, starting from both ordered and disordered initial states. The two-time correlation function $A(t^{\prime },t)$ is measured, and aging phenomena are investigated. The power-law correction in the spatial correlation length $\xi \left(t\right)$ for relaxation with an ordered initial state and the logarithmic correction for relaxation with a disordered initial state are carefully analyzed. The scaling functions of $A(t^{\prime },t)$ are then extracted.

The nonequilibrium escape dynamics in a bistable system under the influence of two Gaussian noises, one obtained by recycling, the other with a constant delay time, is shown by numerical simulation to exhibit stochastic synchronization; i.e., under stationary conditions, an appreciable fraction of renewal trajectories gets locked to the noise-recycling delay time. The conditions for optimal synchronization, reminiscent of stochastic resonance, are interpreted at any order within the framework of Kramers’ theory.

Noncoherent structures that develop during UV laser ablation of stretched semicrystalline polymer foils are a very general phenomenon. A thermodynamic model based on stress relaxation within the modified layer of the polymer surface describes the main features of the observed phenomena, and, in particular, the dependence of the period of structures on laser wavelength, fluence, and number of laser pulses.

The effects of dominant sequential interactions are investigated in an exactly solvable feedforward layered neural network model of binary units and patterns near saturation in which the interaction consists of a Hebbian part and a symmetric sequential term. Phase diagrams of stationary states are obtained and a phase of cyclic correlated states of period two is found for a weak Hebbian term, independently of the number of condensed patterns $c$.