We present a technique that identifies truly interacting subsystems of a complex system from multichannel data if the recordings are an unknown linear and instantaneous mixture of the true sources. The method is valid for arbitrary noise structure. For this, a blind source separation technique is proposed that diagonalizes antisymmetrized cross-correlation or cross-spectral matrices. The resulting decomposition finds truly interacting subsystems blindly and suppresses any spurious interaction stemming from the mixture. The usefulness of this interacting source analysis is demonstrated in simulations and for real electroencephalography data.

We report on harmonic generation by budding yeast cells (Saccharomyces cerevisiae, ${10}^8\mathrm{cells}∕\mathrm{ml}$) in response to sinusoidal electric fields with amplitudes ranging from zero to $5\mathrm{V}∕\mathrm{cm}$ in the frequency range $10–300\mathrm{Hz}$. The cell-generated harmonics are found to exhibit strong amplitude and frequency dependence. Sodium metavanadate, an inhibitor of the proton pump known as ${\mathrm{H}}^{+}$-ATPase, and glucose, a substrate of ${\mathrm{H}}^{+}$-ATPase, are found to increase harmonic production at low amplitudes while reducing it at large amplitudes. This P-type proton pump can be driven by an oscillatory transmembrane potential, and its nonlinear response is believed to be largely responsible for harmonic production at low frequencies in yeast cells. We find that the observed harmonics show dramatic changes with time and in their field and frequency dependence after perturbing the system by adding an inhibitor, substrate, or membrane depolarizer to the cell suspension.

We show that the site-specific interaction of a probe DNA with the template DNA can be well modeled as an unbiased random jump process, where the probe molecule first nonspecifically binds to the template DNA and then searches for the specific site via unbiased random jump motion on the template DNA. By investigating the effects of increasing the jump size, and the fluctuations in the position of the specific site and the fluctuations in the specific site interval on the affinity-specificity negative correlation, we show that (1) increasing the jump size will in turn increase the affinity of the probe toward its target site on the template DNA, however, with a limiting value—the maximum affinity condition; (2) the degree of supercoiling or condensation of the template DNA as well as the electrostatic interactions between the probe and the template in turn control the jump size associated with the dynamics of the probe on the template DNA; (3) under a maximum specificity condition (therefore with minimum affinity), by introducing an external fluctuation in the relative position of the target site on the template DNA with respect to the probe, one can still improve the affinity rate; (4) on the other hand, one can improve the specificity of the probe toward the target site on the template DNA by introducing external fluctuations in the target-site interval. Finally, we propose the design strategies and optimum experimental conditions to simultaneously enhance the affinity as well as the specificity of probe toward its target site on the template DNA.

The coupled nonlinear dynamics of rotary motor ensembles and an embedding fluid medium are simulated on the basis of Navier-Stokes equations. The model description considers space-dependent rotation of motors and a spatially inhomogeneous motor distribution as well as spatial fluctuations in molecular properties. The mutual influnce of motor rotations and fluid dynamics as well as spatial inhomogeneities of their molecular properties are self-consistently included. Space-time simulations visualize the complex interplay between the fluid dynamics and motor rotation and show that the dynamic coupling to the environment via the velocity field as well as the spatial inhomogeneity and distribution of rotors determines the overall behavior of the motor complex. Depending on the initial molecular distribution, rotation frequency, and fluid dynamics a spatial self-organization or a chaotic behavior may arise.

We study the mean length $\ell \left(k\right)$ of the shortest paths between a vertex of degree $k$ and other vertices in growing networks, where correlations are essential. In a number of deterministic scale-free networks we observe a power-law correction to a logarithmic dependence, $\ell \left(k\right)=A\ln [N∕k^{(\gamma -1)∕2}]-C{k}^{\gamma -1}∕N+\cdots$ in a wide range of network sizes. Here $N$ is the number of vertices in the network, $\gamma$ is the degree distribution exponent, and the coefficients $A$ and $C$ depend on a network. We compare this law with a corresponding $\ell \left(k\right)$ dependence obtained for random scale-free networks growing through the preferential attachment mechanism. In stochastic and deterministic growing trees with an exponential degree distribution, we observe a linear dependence on degree, $\ell \left(k\right)\cong A\ln N-Ck$. We compare our findings for growing networks with those for uncorrelated graphs.

We use photoelectron emission microscopy (PEEM) measurements to study the spatiotemporal patterns obtained for the $\mathrm{CO}$ oxidation reaction on $\mathrm{Ir}\left(111\right)$ as a function of the noise strength we superpose on the $\mathrm{CO}$ and the oxygen fractions of the constant total reactant gas flux. The investigations are focused on the bistable regime this reaction displays including its monostable vicinity. Simultaneously we analyze numerically the underlying reaction-diffusion (RD) equations in two spatial dimensions. For intrinsic and/or small strength of the external noise we find transitions from the locally stable to the globally stable branch via slow nucleation and growth of islands of the globally stable state: oxygen or $\mathrm{CO}$, respectively. With increasing noise strength the number of islands as well as their growth rate increases. These phenomena are very well reproduced by numerical calculations of the RD model. For sufficiently large noise strength we observe bursts from $\mathrm{CO}$ rich to oxygen rich and back as well as switching between the two states. While such phenomena are also obtained from the model calculations, their experimentally observed spatial scales were not satisfactorily reproduced using the same approach as for the lower noise strengths.

A multiscale approach is used to derive stochastic amplitude and phase dynamics for a canonical noise-sensitive model exhibiting coherence resonance. Explicit expressions for the dependence on noise levels and model type are compared with computational coherence measures.

We investigate the connection between local and global dynamics in the Fermi-Pasta-Ulam (FPU) $\beta$ model from the point of view of stability of its simplest periodic orbits (SPO’s). In particular, we show that there is a relatively high-$q$ mode $[q=2(N+1)∕3]$ of the linear lattice, having one particle fixed every two oppositely moving ones (called SPO2 here), which can be exactly continued to the nonlinear case for $N=5+3m$, $m=0,1,2,\dots$, and whose first destabilization $E_{2u}$, as the energy (or $\beta$) increases for any fixed $N$, practically coincides with the onset of a “weak” form of chaos preceding the breakdown of FPU recurrences, as predicted recently in a similar study of the continuation of a very low $(q=3)$ mode of the corresponding linear chain. This energy threshold per particle behaves like $\frac{E_{2u}}{N}\propto N^{-2}$. We also follow exactly the properties of another SPO [with $q=(N+1)∕2$] in which fixed and moving particles are interchanged (called SPO1 here) and which destabilizes at higher energies than SPO2, since $\frac{E_{1u}}{N}\propto N^{-1}$. We find that, immediately after their first destabilization, these SPO’s have different (positive) Lyapunov spectra in their vicinity. However, as the energy increases further (at fixed $N$), these spectra converge to the same exponentially decreasing function, thus providing strong evidence that the chaotic regions around SPO1 and SPO2 have “merged” and large-scale chaos has spread throughout the lattice. Since these results hold for $N$ arbitrarily large, they suggest a direct approach by which one can use local stability analysis of SPO’s to estimate the energy threshold at which a transition to ergodicity occurs and thermodynamic properties such as Kolmogorov-Sinai entropies per particle can be computed for similar one-dimensional lattices.

We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is applied to the study of complex patterns generated by coupled map lattices, which are characterized by measures of complexity based on SRPs. We show that the complexity measures we propose for SRPs provide a systematic way of investigating the distribution of spatially coherent structures, such as synchronization domains, in lattice profiles. This approach has potential for many more applications, e.g., in surface roughness analyzes.

The dense flow of air bubbles in a two-dimensional silo (through an aperture $D$) filled with a liquid is studied experimentally. A particle tracking technique has been used to bring out the main properties of the flow: displacements of the bubbles, transverse, and axial velocities. The behavior of the air bubbles is observed to present similarities with nondeformable solid grains in a granular flow. Nevertheless, a correlation between the bubble velocities and their deformations has been evidenced. Moreover, a new discharge law (Beverloo like) must be considered for such a system, where the flow rate is observed to vary as $D^{1∕2}$ and depends on the deformability of the particles.

Experiments on the zigzag transition of finite dust clusters are presented. There, microspheres have been confined in an anisotropic trap in the sheath of a radio-frequency discharge plasma. Transitions of the clusters from a linear chain into a zigzag configuration are observed by increasing the particle number in the chain or by variation of the anisotropy of the confinement. The equilibrium configurations of the finite clusters, as well as the dynamical properties and the stability behavior near the transition have been investigated from a normal mode analysis. Furthermore, the longitudinal and transverse dispersion of the normal modes in the one-dimensional (1D) chain has been derived.

A model for chaotic mixing has been formulated and tested. The advection of a passive scalar by laminar flows with high Péclet numbers is modeled by a finite-volume method on a coarse grid. The scales which are smaller than the increment of the grid are modeled by an approximate subgrid model. The artificial diffusivity of the finite-difference method plays a twofold role. It prevents the formation of spurious oscillations of the solution and also models the transport of the variation of the scalar from the large to subgrid modes.

This paper discusses an application of a random network with a variable number of links and traps to the elimination of drug molecules from the body by the liver. The nodes and links represent the transport vessels, and the traps represent liver cells with metabolic enzymes that eliminate drug molecules. By varying the number and configuration of links and nodes, different disease states of the liver related to vascular damage have been simulated, and the effects on the rate of elimination of a drug have been investigated. Results of numerical simulations show the prevalence of exponential decay curves with rates that depend on the concentration of links. In the case of fractal lattices at the percolation threshold, we find that the decay of the concentration is described by exponential functions for high trap concentrations but transitions to stretched exponential behavior at low trap concentrations.

We perform three-dimensional simulations of fracture growth in a three-layered plate model with an embedded heterogeneous layer under horizontal biaxial stretch (representing stretch from directional to isotropic) by the finite element approach. The fractures develop under a quasistatical, slowly increasing biaxial strain. The material inhomogeneities are accounted for by assigning each element a failure threshold that is defined by a given statistical distribution. A universal scale law of fracture spacing to biaxial strain in terms of principal stress ratio is well demonstrated in a three-dimensional fashion. The numerically obtained fracture patterns show a continuous pattern transition from parallel fractures, laddering fracture to polygonal fractures, which depends strongly on the far-field loading conditions in terms of principal stress ratio $(\lambda ={\sigma }_2∕{\sigma }_1)$, from uniaxial $(\lambda =0)$, anisotropic $(0<\lambda <1)$ to isotropic stretch $(\lambda =1)$. We find that, except for further opening of existing fractures after they are well-developed (saturation), new fractures may also initiate and propagate along the interface between layers, which may serve as another mechanism to accommodate additional strain for fracture saturated layers.

We propose an efficient method of generating long-range correlations in large systems. The development of this method was motivated by the problem of constructing an optimal model for a large-scale porous medium. There are typically long-range correlations in the properties of such porous media, such as their permeability and porosity, for which there are usually only limited data. The optimal model must not only honor (preserve) the available data and their correlation function, but also accurately predict the future behavior of fluid flow in the media. We formulate the problem of generating the long-range correlations as one of optimization, and utilize simulated annealing to generate a $d$-dimensional array which contains the correlations and honors the existing data. The optimization process is based on the data’s correlation function. The method is, therefore, free of the many numerical difficulties and/or limitations that most previous techniques suffer from. It is completely general and may be used for generating long-range correlations with any type of correlation function, in both isotropic and anisotropic media. Representative examples are presented, and the method’s efficiency and accuracy are discussed.

The concept of inverse statistics in turbulence has attracted much attention in recent years. It is argued that the scaling exponents of the direct structure functions and the inverse structure functions satisfy an inversion formula. This proposition has already been verified by numerical data using the shell model. However, no direct evidence was reported for experimental three-dimensional turbulence. We propose to test the inversion formula using experimental data of three-dimensional fully developed turbulence by considering the energy dissipation rates instead of the usual efforts on the structure functions. The moments of the exit distances are shown to exhibit nice multifractality. The inversion formula between the direct and inverse exponents is then verified.

The near-field dynamics of a femtosecond Bessel beam propagating in a Kerr nonlinear medium (fused silica) is investigated both numerically and experimentally. We demonstrate that the input Bessel beam experiences strong nonlinear reshaping. Due to the combined action of self-focusing and nonlinear losses the reshaped beam exhibits a radial compression and reduced visibility of the Bessel oscillations. Moreover, we show that the reshaping process starts from the intense central core and gradually replaces the Bessel beam profile during propagation, highlighting the conical geometry of the energy flow.

A lattice Boltzmann model for mixture modeling is developed by applying the multiple-relaxation-time (MRT) approach to the Hamel model, which allows one to derive from a general framework different model equations independently proposed, like the Gross-Krook model and the Sirovich model. By imposing some physical constraints, the MRT lattice-Boltzmann Hamel model reduces to the generalized MRT lattice-Boltzmann Gross-Krook model (involving the local Maxwellian centered on the barycentric velocity), which allows one to tune independently the species diffusivity, the mixture kinematic viscosity, and the mixture bulk viscosity. Reducing the number of moving particles over the total is possible to deal effectively with mass particle ratios far from unity and, for this reason, to model the pressure-driven diffusion. A convenient numerical approach is proposed for solving the developed model, which essentially widens the stability range of conventional schemes in terms of dimensionless relaxation frequencies, by solving explicitly the advection operator together with the nonlinear terms of the collisional operator and solving implicitly the residual linear terms. In this way, the calculations are drastically reduced and the operative matrices can be computed once for all, at the beginning of the calculation (implying moderate additional computational demand). Following this approach, a semi-implicit-linearized backward Euler scheme, ideal for parallel implementations, is proposed. In order to achieve the previous results, the asymptotic analysis, recently suggested for analyzing the macroscopic equations corresponding to lattice-Boltzmann schemes in the low-Mach-number limit, proves to be an effective tool. Some numerical tests are reported for proving the consistency of the proposed method with both the Fick model and Maxwell-Stefan model in the macroscopic limit.

We consider the influence of population size on the accuracy of diffusion quantum Monte Carlo simulations that employ descendant weighting or forward walking techniques to compute expectation values of observables that do not commute with the Hamiltonian. We show that for a simple model system, the $d$-dimensional isotropic harmonic oscillator, the population size must increase rapidly with $d$ in order to ensure that the simulations produce accurate results. When the population size is too small, expectation values computed using descendant-weighted diffusion quantum Monte Carlo simulations exhibit significant systematic biases.

We quantify, within mode coupling theory, how changes in the liquid structure affect that of the glass. Apart from the known sensitivity to the structure factor $S\left(q\right)$ at wave vectors around the first sharp diffraction peak $q_0$, we find a strong (and inverted) response to structure at wave vectors below this peak: an increase in $S(q_0∕2)$ lowers the degree of arrest over a wide $q$-range. This strong sensitivity to “caged cage” packing effects, on length scales of order $2d$, is much weaker in attractive glasses where short-range bonding dominates the steric caging effect.