To quantitatively predict the mechanical response and mechanically induced remodeling of red blood cells, we developed a multiscale method to correlate distributions of internal stress with overall cell deformation. This method consists of three models at different length scales: in the complete cell level the membrane is modeled as two distinct layers of continuum shells using finite element method (Level III), in which the skeleton-bilayer interactions are depicted as a slide in the lateral (i.e., in-plane) direction (caused by the mobility of the skeleton-bilayer pinning points) and a normal contact force; the constitutive laws of the inner layer (the protein skeleton) are obtained from a molecular-based model (Level II); the mechanical properties of the spectrin (Sp, a key component of the skeleton), including its folding/unfolding reactions, are obtained with a stress-strain model (Level I). Model verification is achieved through comparisons with existing numerical and experimental studies in terms of the resting shape of the cell as well as cell deformations induced by micropipettes and optical tweezers. Detailed distributions of the interaction force between the lipid bilayer and the skeleton that may cause their dissociation and lead to phenomena such as vesiculation are predicted. Specifically, our model predicts correlation between the occurrence of Sp unfolding and increase in the mechanical load upon individual skeleton-bilayer pinning points. Finally a simulation of the necking process after skeleton-bilayer dissociation, a precursor of vesiculation, is conducted.

We study the correlated Wishart ensembles in the context of time series analysis. We are interested in the statistics of eigenlevels, viz. variables associated with independent eigenmodes in the system. The motivation of this work is to study the effect of time series correlations on the Wishart ensembles. In this connection, we derive the level density and the two-point function for the correlated Wishart ensembles by using the binary correlation method. Using our analytic results we analyze spectra of autocovariance matrices derived from single variable stationary time series. We consider the stochastic time series of Gaussian variables with exponentially decaying correlations and time series of chaotic maps, viz. the Arnold map, the Standard map and the stadium billiard map. In both cases, correlated time series are encountered and analyzed under the framework of random matrix theory. It is shown that the eigenlevel statistics for the chaotic maps follow closely those of correlated Wishart ensembles. It is indicated that the presence of collective modes in the spectra of autocovariance matrices is related to the integrability of the system.

Recently, it has been observed [Md. Nurujjaman et al., Phy. Rev. E 80, 015201(R) (2009)] that in an excitable system, one can maintain noise-induced coherency in the coherence resonance by blocking the destructive effect of the noise on the system at higher noise level. This phenomenon of constant coherence resonance (CCR) cannot be explained by the existing way of simulation of the model equations of an excitable system with added noise. In this paper, we have proposed a general model which explains the noise-induced resonance phenomenon CCR as well as coherence resonance (CR) and stochastic resonance (SR). The simulation has been carried out considering the basic mechanism of noise-induced resonance phenomena: noise only perturbs the system control parameter to excite coherent oscillations, taking proper precautions so that the destructive effect of noise does not affect the system. In this approach, the CR has been obtained from the interference between the system output and noise and the SR has been obtained by adding noise and a subthreshold signal. This also explains the observation of the frequency shift of coherent oscillations in the CCR with noise level.

A network of phase-coupled oscillators constitutes a system in which excitable $2\pi$ phase slips can be induced by noise. We show that such an excitation in one of the oscillators can be regenerated by subsequent oscillators and become self-sustained for certain topologies. We focus on the simplest such topology: two mutually coupled oscillators. Our analysis is bolstered by an experimental confirmation of the phenomenon via a pair of mutually delay coupled quantum-dot lasers. Both the intensities and phases of the laser outputs were measured confirming the interpretation.

Locomotion and generation of flow at low Reynolds number are subject to severe limitations due to the irrelevance of inertia: the “scallop theorem” requires that the system have at least two degrees of freedom, which move in non-reciprocal fashion, i.e. breaking time-reversal symmetry. We show here that a minimal model consisting of just two spheres driven by harmonic potentials is capable of generating flow. In this pump system the two degrees of freedom are the mean and relative positions of the two spheres. We have performed and compared analytical predictions, numerical simulation and experiments, showing that a time-reversible drive is sufficient to induce flow.

In a recent work, Wyss et al. [Phys. Rev. Lett. 98, 238303 (2007)] have noted a property of “soft solids” under oscillatory shear, the so-called strain-rate frequency superposition. We extend this study to the case of soft solids under large-amplitude oscillatory shear (LAOS). We show results from LAOS studies in a monodisperse hydrogel suspension, an aqueous gel, and a biopolymer suspension and show that constant strain-rate frequency sweep measurements with soft solids can be superimposed onto master curves for higher harmonic moduli with the same shift factors as for the linear viscoelastic moduli. We show that the behavior of higher harmonic moduli at low frequencies in constant strain-rate frequency sweep measurements is similar to that at large strain amplitude in strain-amplitude sweep tests. We show surface plots of the harmonic moduli and the energy dissipation rate per unit volume in LAOS for soft solids and show experimentally that the energy dissipated per unit volume depends on the first harmonic loss modulus alone, in both the linear and the nonlinear viscoelastic regime.

The principle of energy conservation leads to a generalized choice of transition probability in a piecewise adiabatic representation of quantum(-classical) dynamics. Significant improvement (almost an order of magnitude, depending on the parameters of the calculation) over previous schemes is achieved. Perspectives for theoretical calculations in coherent many-body systems are opened.

The author investigates the onset of patterns in vertically oscillated layers of dissipative particles using numerical solutions of continuum equations to Navier-Stokes order. Above a critical accelerational amplitude of the cell, standing waves form stripe patterns which oscillate subharmonically with respect to the cell. Continuum simulations neglecting interparticle friction yield pattern wavelengths consistent with experiments using frictional particles. However, the critical acceleration for standing-wave formation is approximately 10% lower in continuum simulations without added noise than in molecular-dynamics simulations. This Brief Report incorporates fluctuating hydrodynamics theory into continuum simulations by adding noise terms with no fit parameters; this modification yields a critical acceleration in agreement with molecular-dynamics simulations.

Small-world networks describe many important practical systems among which neural networks consisting of excitable nodes are the most typical ones. In this paper we study self-sustained oscillations of target waves in excitable small-world networks. A dominant phase-advanced driving (DPAD) method, which is generally applicable for analyzing all oscillatory complex networks consisting of nonoscillatory nodes, is proposed to reveal the self-organized structures supporting this type of oscillations. The DPAD method explicitly explores the oscillation sources and wave propagation paths of the systems, which are otherwise deeply hidden in the complicated patterns of randomly distributed target groups. Based on the understanding of the self-organized structure, the oscillatory patterns can be controlled with an extremely high efficiency.

We develop a formalism to study linearized perturbations around the equilibria of a pure-exchange economy. With the use of mean-field theory techniques, we derive equations for the flow of products in an economy driven by heterogeneous preferences and probabilistic interaction between agents. We are able to show that if the economic agents have static preferences, which are also homogeneous in any of the steady states, the final wealth distribution is independent of the dynamics of the nonequilibrium theory. In particular, it is completely determined in terms of the initial conditions and it is independent of the probability, and the network of interaction between agents. We show that the main effect of the network is to determine the relaxation time via the usual eigenvalue gap as in random walks on graphs.

We investigate the route to synchronization in an ensemble of uncoupled chaotic oscillators under common noise. Previous works have demonstrated that, as the common-noise amplitude is increased, both chaotic phase synchronization and complete synchronization can occur. Our study reveals an intermediate state of synchronization in between these two types of synchronization. A statistical measure is introduced to characterize this noise-induced synchronization state and the dynamical origin of the transition to it is elucidated based on the Lyapunov dimension of the set formed by all oscillator states.

The resistive decay of chains of three interlocked magnetic flux rings is considered. Depending on the relative orientation of the magnetic field in the three rings, the late-time decay can be either fast or slow. Thus, the qualitative degree of tangledness is less important than the actual value of the linking number or, equivalently, the net magnetic helicity. Our results do not suggest that invariants of higher order than that of the magnetic helicity need to be considered to characterize the decay of the field.

Normal-incidence left-handed metamaterials (LHMs) based on symmetrically connected split-ring resonators (SC-SRRs) were proposed and investigated numerically and experimentally. The SC-SRR, which can be easily fabricated by conventional printed circuit board technology, is composed of metallic patterns connected by metalized vias through the dielectric substrate. Under normal incidence, SC-SRR exhibits strong magnetic response, leading to negative permeability. By combing SC-SRRs with metallic wires, a normal-incidence LHM was realized. Both the simulation and experiment results demonstrated left-handed properties of the SC-SRR/wire LHM. The design method paved new ways of realizing magnetic and even electric metamaterials.

We present a framework for the stochastic features of the polarization state of an electromagnetic wave propagating through the optical medium with both deterministic (controlled) and disordered birefringence. In this case, the Stokes parameters obey a Langevin-type equation on the Poincaré sphere. The functional integral method provides for a natural tool to derive the Fokker-Planck equation for the probability distribution of the Stokes parameters. We solve the Fokker-Planck equation in the case of a random anisotropic active medium submitted to a homogeneous electromagnetic field. The possible dissipation and relaxation phenomena are studied in general and in various cases, and we give hints about how to validate experimentally the corresponding phenomenological equations.

Detrended fluctuation analysis (DFA) is an improved method of classical fluctuation analysis for nonstationary signals where embedded polynomial trends mask the intrinsic correlation properties of the fluctuations. To better identify the intrinsic correlation properties of real-world signals where a large amount of data is missing or removed due to artifacts, we investigate how extreme data loss affects the scaling behavior of long-range power-law correlated and anticorrelated signals. We introduce a segmentation approach to generate surrogate signals by randomly removing data segments from stationary signals with different types of long-range correlations. The surrogate signals we generate are characterized by four parameters: (i) the DFA scaling exponent $\alpha$ of the original correlated signal $u\left(i\right)$, (ii) the percentage $p$ of the data removed from $u\left(i\right)$, (iii) the average length $\mu$ of the removed (or remaining) data segments, and (iv) the functional form $P\left(l\right)$ of the distribution of the length $l$ of the removed (or remaining) data segments. We find that the global scaling exponent of positively correlated signals remains practically unchanged even for extreme data loss of up to 90%. In contrast, the global scaling of anticorrelated signals changes to uncorrelated behavior even when a very small fraction of the data is lost. These observations are confirmed on two examples of real-world signals: human gait and commodity price fluctuations. We further systematically study the local scaling behavior of surrogate signals with missing data to reveal subtle deviations across scales. We find that for anticorrelated signals even 10% of data loss leads to significant monotonic deviations in the local scaling at large scales from the original anticorrelated to uncorrelated behavior. In contrast, positively correlated signals show no observable changes in the local scaling for up to 65% of data loss, while for larger percentage of data loss, the local scaling shows overestimated regions (with higher local exponent) at small scales, followed by underestimated regions (with lower local exponent) at large scales. Finally, we investigate how the scaling is affected by the average length, probability distribution, and percentage of the remaining data segments in comparison to the removed segments. We find that the average length ${\mu }_r$ of the remaining segments is the key parameter which determines the scales at which the local scaling exponent has a maximum deviation from its original value. Interestingly, the scales where the maximum deviation occurs follow a power-law relationship with ${\mu }_r$. Whereas the percentage of data loss determines the extent of the deviation. The results presented in this paper are useful to correctly interpret the scaling properties obtained from signals with extreme data loss.

The theoretical treatment of transport in a disordered system in the presence of a system-wide force field $\mathcal{F}\left(\mathbf{x}\right)$ or spatially varying macroscopic velocity field $\mathbf{v}\left(\mathbf{x}\right)$ is developed in the framework of continuous time random walk (CTRW). The physical basis of CTRW and related fractional derivative equations relies on a mapping of the aggregate of transition rates $w\left(\mathbf{s},{\mathbf{s}}^{\prime }\right)$, between sites $\mathbf{s}$ and ${\mathbf{s}}^{\prime }$, in the Master equation describing the system kinetics, onto a joint probability distribution function $\psi \left(\mathbf{s},t\right)$. This distribution is calculated from the ensemble average of a position-dependent functional of $w\left(\mathbf{s},{\mathbf{s}}^{\prime }\right)$; the procedure is effective when the scale of heterogeneities is much smaller than the system size. However, statistical homogeneity does not hold in the presence of large heterogeneities, which control the macroscopic $\mathbf{v}\left(\mathbf{x}\right)$, or in the case of an interaction of $\mathcal{F}\left(\mathbf{x}\right)$ with the transition rates. The transport equation, incorporating large-scale heterogeneity, involves the use of a local ensemble average to obtain a position-dependent $\psi \left(\mathbf{s},t;\mathbf{x}\right)$; this determines a memory function, $M\left(t;\mathbf{x}\right)$, which is convoluted with the advection-dispersion operator. A prototype transport equation for a system with statistical inhomogeneity is developed as an integrodifferential equation. It is solved numerically for particles migrating with a steady-state Darcy velocity $\mathbf{v}\left(\mathbf{x}\right)$, determined for different permeability fields and boundary conditions. The nature of the solutions as a function of key transport parameters (e.g., a characteristic time $t_c$) is explored, and solutions are also compared to those of the advection-dispersion equation for $\mathbf{v}\left(\mathbf{x}\right)$ and to a laboratory experiment. This transport equation is in contrast to the fractional Fokker-Planck equation, which is based on a decoupling of $\mathcal{F}\left(\mathbf{x}\right)$ or $\mathbf{v}\left(\mathbf{x}\right)$ with the transition rates $w\left(\mathbf{s},{\mathbf{s}}^{\prime }\right)$. Further, an analytic expression for the effect of a variance of the ensemble average on the solution of the CTRW transport equation is derived.

Recent studies reported continuous shortening of the pitch from more than four layers to less than four layers in the helicoidally modulated tilted $\text{Sm}{C}_{\alpha }^{\ast }$ phase. In a different system, the reversed phase sequence was found: the ferroelectric tilted $\text{Sm}{C}^{\ast }$ phase appeared below the four-layer $\text{Sm}{C}_{FI2}^{\ast }$ phase upon cooling. In this contribution we quantitatively explain the behavior within the discrete phenomenological model and we found that both behaviors are the consequence of the same reason: the quadrupolar interlayer interactions.

We present a systematic study of the dynamical scaling process leading to the establishment of the Kolmogorov-Zakharov (KZ) spectrum in weak three-wave turbulence. In the finite-capacity case, in which the transient spectrum reaches infinite frequency in finite time, the dynamical scaling exponent is anomalous in the sense that it cannot be determined from dimensional considerations. As a consequence, the transient spectrum preceding the establishment of the steady state is steeper than the KZ spectrum. Constant energy flux is actually established from right to left in frequency space after the singularity of the transient solution. From arguments based on entropy production, a steeper transient spectrum is heuristically plausible.

We study the collective dynamics of mobile species under cyclic competition by breaking the symmetry in the initial populations and examining the basins of the two distinct asymptotic states: extinction and coexistence, the latter maintaining biodiversity. We find a rich dependence of dynamical properties on initial conditions. In particular, for high mobility, only extinction basins exist and they are spirally entangled, but a basin of coexistence emerges when the mobility parameter is decreased through a critical value, whose area increases monotonically as the parameter is further decreased. The structure of extinction basins for high mobility can be predicted by a mean-field theory. These results provide a more comprehensive picture for the fundamental issue of species coexistence than previously achieved.

The homogeneous plaquette Ising model in two and three dimensions is investigated by means of Monte Carlo simulations. By introducing a suitable order parameter for the two-dimensional lattice, and the finite-size scaling of the corresponding fourth-order cumulant, it is found that, consistent with the previous theoretical indications, the model in two dimensions is disordered at finite temperature and exhibits a zero-temperature phase transition characteristic of the one-dimensional Ising model with an essential (exponential) singularity of the order-parameter susceptibility as opposed to a Curie-law (power-law) divergence. In three dimensions, however, the model is believed to have a first-order phase transition at $T_c\simeq 3.6$ screened by strong metastability leading to a so-called “glassy transition” at $T\simeq 3.4$ when subjected to slow cooling. By computing the configurational entropy $S_c\equiv S\left(\text{liquid}\right)-S\left(\text{crystal}\right)$ in the supercooled temperature range via thermodynamic integration of the internal energy results, the Kauzmann temperature defined as that temperature where the extrapolated configurational entropy $S_c\left(T\right)$ vanishes, is estimated to be $T_K\simeq 3.18$. By finding ways to estimate the equilibration time of the supercooled liquid and the nucleation time of the stable crystal droplets, it is shown that $T\simeq 3.4$ is indeed the limit of stability or the effective spinodal temperature $T_{\text{sp}}$, at which the two time-scales associated with the quasiequilibration of the supercooled liquid, ${\tau }_{\text{eq}}$, and the nucleation of the stable crystal droplets, ${\tau }_{\text{nuc}}$, cross one another, with the former rising above the latter such that the supercooled liquid state becomes physically irrelevant below $T_{\text{sp}}\simeq 3.4$ and the impending entropy crisis at $T_K\simeq 3.18$ $\left(<T_{\text{sp}}\right)$ is thus avoided. Hence, what is sometimes called “glassy temperature,” is really a kinetic spinodal temperature that may be regarded as the remnant of the mean-field spinodal.